---
_id: '10548'
abstract:
- lang: eng
text: "Consider a linear elliptic partial differential equation in divergence form
with a random coefficient field. The solution operator displays fluctuations around
its expectation. The recently developed pathwise theory of fluctuations in stochastic
homogenization reduces the characterization of these fluctuations to those of
the so-called standard homogenization commutator. In this contribution, we investigate
the scaling limit of this key quantity: starting\r\nfrom a Gaussian-like coefficient
field with possibly strong correlations, we establish the convergence of the rescaled
commutator to a fractional Gaussian field, depending on the decay of correlations
of the coefficient field, and we\r\ninvestigate the (non)degeneracy of the limit.
This extends to general dimension $d\\ge1$ previous results so far limited to
dimension $d=1$, and to the continuum setting with strong correlations recent
results in the discrete iid case."
acknowledgement: The authors thank Ivan Nourdin and Felix Otto for inspiring discussions.
The work of MD is financially supported by the CNRS-Momentum program. Financial
support of AG is acknowledged from the European Research Council under the European
Community’s Seventh Framework Programme (FP7/2014-2019 Grant Agreement QUANTHOM
335410).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Mitia
full_name: Duerinckx, Mitia
last_name: Duerinckx
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Antoine
full_name: Gloria, Antoine
last_name: Gloria
citation:
ama: Duerinckx M, Fischer JL, Gloria A. Scaling limit of the homogenization commutator
for Gaussian coefficient fields. Annals of applied probability. 2022;32(2):1179-1209.
doi:10.1214/21-AAP1705
apa: Duerinckx, M., Fischer, J. L., & Gloria, A. (2022). Scaling limit of the
homogenization commutator for Gaussian coefficient fields. Annals of Applied
Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-AAP1705
chicago: Duerinckx, Mitia, Julian L Fischer, and Antoine Gloria. “Scaling Limit
of the Homogenization Commutator for Gaussian Coefficient Fields.” Annals
of Applied Probability. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AAP1705.
ieee: M. Duerinckx, J. L. Fischer, and A. Gloria, “Scaling limit of the homogenization
commutator for Gaussian coefficient fields,” Annals of applied probability,
vol. 32, no. 2. Institute of Mathematical Statistics, pp. 1179–1209, 2022.
ista: Duerinckx M, Fischer JL, Gloria A. 2022. Scaling limit of the homogenization
commutator for Gaussian coefficient fields. Annals of applied probability. 32(2),
1179–1209.
mla: Duerinckx, Mitia, et al. “Scaling Limit of the Homogenization Commutator for
Gaussian Coefficient Fields.” Annals of Applied Probability, vol. 32,
no. 2, Institute of Mathematical Statistics, 2022, pp. 1179–209, doi:10.1214/21-AAP1705.
short: M. Duerinckx, J.L. Fischer, A. Gloria, Annals of Applied Probability 32 (2022)
1179–1209.
date_created: 2021-12-16T12:10:16Z
date_published: 2022-04-28T00:00:00Z
date_updated: 2023-08-02T13:35:06Z
day: '28'
department:
- _id: JuFi
doi: 10.1214/21-AAP1705
external_id:
arxiv:
- '1910.04088'
isi:
- '000791003700011'
intvolume: ' 32'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1910.04088
month: '04'
oa: 1
oa_version: Preprint
page: 1179-1209
publication: Annals of applied probability
publication_identifier:
issn:
- 1050-5164
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Scaling limit of the homogenization commutator for Gaussian coefficient fields
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 32
year: '2022'
...
---
_id: '11842'
abstract:
- lang: eng
text: We consider the flow of two viscous and incompressible fluids within a bounded
domain modeled by means of a two-phase Navier–Stokes system. The two fluids are
assumed to be immiscible, meaning that they are separated by an interface. With
respect to the motion of the interface, we consider pure transport by the fluid
flow. Along the boundary of the domain, a complete slip boundary condition for
the fluid velocities and a constant ninety degree contact angle condition for
the interface are assumed. In the present work, we devise for the resulting evolution
problem a suitable weak solution concept based on the framework of varifolds and
establish as the main result a weak-strong uniqueness principle in 2D. The proof
is based on a relative entropy argument and requires a non-trivial further development
of ideas from the recent work of Fischer and the first author (Arch. Ration. Mech.
Anal. 236, 2020) to incorporate the contact angle condition. To focus on the effects
of the necessarily singular geometry of the evolving fluid domains, we work for
simplicity in the regime of same viscosities for the two fluids.
acknowledgement: The authors warmly thank their former resp. current PhD advisor Julian
Fischer for the suggestion of this problem and for valuable initial discussions
on the subjects of this paper. This project has received funding from the European
Research Council (ERC) under the European Union’s Horizon 2020 research and innovation
programme (grant agreement No 948819) , and from the Deutsche Forschungsgemeinschaft
(DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1
– 390685813.
article_number: '93'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
- first_name: Alice
full_name: Marveggio, Alice
id: 25647992-AA84-11E9-9D75-8427E6697425
last_name: Marveggio
citation:
ama: Hensel S, Marveggio A. Weak-strong uniqueness for the Navier–Stokes equation
for two fluids with ninety degree contact angle and same viscosities. Journal
of Mathematical Fluid Mechanics. 2022;24(3). doi:10.1007/s00021-022-00722-2
apa: Hensel, S., & Marveggio, A. (2022). Weak-strong uniqueness for the Navier–Stokes
equation for two fluids with ninety degree contact angle and same viscosities.
Journal of Mathematical Fluid Mechanics. Springer Nature. https://doi.org/10.1007/s00021-022-00722-2
chicago: Hensel, Sebastian, and Alice Marveggio. “Weak-Strong Uniqueness for the
Navier–Stokes Equation for Two Fluids with Ninety Degree Contact Angle and Same
Viscosities.” Journal of Mathematical Fluid Mechanics. Springer Nature,
2022. https://doi.org/10.1007/s00021-022-00722-2.
ieee: S. Hensel and A. Marveggio, “Weak-strong uniqueness for the Navier–Stokes
equation for two fluids with ninety degree contact angle and same viscosities,”
Journal of Mathematical Fluid Mechanics, vol. 24, no. 3. Springer Nature,
2022.
ista: Hensel S, Marveggio A. 2022. Weak-strong uniqueness for the Navier–Stokes
equation for two fluids with ninety degree contact angle and same viscosities.
Journal of Mathematical Fluid Mechanics. 24(3), 93.
mla: Hensel, Sebastian, and Alice Marveggio. “Weak-Strong Uniqueness for the Navier–Stokes
Equation for Two Fluids with Ninety Degree Contact Angle and Same Viscosities.”
Journal of Mathematical Fluid Mechanics, vol. 24, no. 3, 93, Springer Nature,
2022, doi:10.1007/s00021-022-00722-2.
short: S. Hensel, A. Marveggio, Journal of Mathematical Fluid Mechanics 24 (2022).
date_created: 2022-08-14T22:01:45Z
date_published: 2022-08-01T00:00:00Z
date_updated: 2023-11-30T13:25:02Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00021-022-00722-2
ec_funded: 1
external_id:
arxiv:
- '2112.11154'
isi:
- '000834834300001'
file:
- access_level: open_access
checksum: 75c5f286300e6f0539cf57b4dba108d5
content_type: application/pdf
creator: cchlebak
date_created: 2022-08-16T06:55:22Z
date_updated: 2022-08-16T06:55:22Z
file_id: '11848'
file_name: 2022_JMathFluidMech_Hensel.pdf
file_size: 2045570
relation: main_file
success: 1
file_date_updated: 2022-08-16T06:55:22Z
has_accepted_license: '1'
intvolume: ' 24'
isi: 1
issue: '3'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Journal of Mathematical Fluid Mechanics
publication_identifier:
eissn:
- 1422-6952
issn:
- 1422-6928
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '14587'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety
degree contact angle and same viscosities
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 24
year: '2022'
...
---
_id: '11858'
abstract:
- lang: eng
text: "This paper is a continuation of Part I of this project, where we developed
a new local well-posedness theory for nonlinear stochastic PDEs with Gaussian
noise. In the current Part II we consider blow-up criteria and regularization
phenomena. As in Part I we can allow nonlinearities with polynomial growth and
rough initial values from critical spaces. In the first main result we obtain
several new blow-up criteria for quasi- and semilinear stochastic evolution equations.
In particular, for semilinear equations we obtain a Serrin type blow-up criterium,
which extends a recent result of Prüss–Simonett–Wilke (J Differ Equ 264(3):2028–2074,
2018) to the stochastic setting. Blow-up criteria can be used to prove global
well-posedness for SPDEs. As in Part I, maximal regularity techniques and weights
in time play a central role in the proofs. Our second contribution is a new method
to bootstrap Sobolev and Hölder regularity in time and space, which does not require
smoothness of the initial data. The blow-up criteria are at the basis of these
new methods. Moreover, in applications the bootstrap results can be combined with
our blow-up criteria, to obtain efficient ways to prove global existence. This
gives new results even in classical \U0001D43F2-settings, which we illustrate
for a concrete SPDE. In future works in preparation we apply the results of the
current paper to obtain global well-posedness results and regularity for several
concrete SPDEs. These include stochastic Navier–Stokes equations, reaction– diffusion
equations and the Allen–Cahn equation. Our setting allows to put these SPDEs into
a more flexible framework, where less restrictions on the nonlinearities are needed,
and we are able to treat rough initial values from critical spaces. Moreover,
we will obtain higher-order regularity results."
acknowledgement: "The authors thank Emiel Lorist for helpful comments. The authors
thank the anonymous referees for their helpful remarks to improve the presentation.\r\nOpen
access funding provided by Institute of Science and Technology (IST Austria)."
article_number: '56'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Antonio
full_name: Agresti, Antonio
id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72
last_name: Agresti
orcid: 0000-0002-9573-2962
- first_name: Mark
full_name: Veraar, Mark
last_name: Veraar
citation:
ama: Agresti A, Veraar M. Nonlinear parabolic stochastic evolution equations in
critical spaces part II. Journal of Evolution Equations. 2022;22(2). doi:10.1007/s00028-022-00786-7
apa: Agresti, A., & Veraar, M. (2022). Nonlinear parabolic stochastic evolution
equations in critical spaces part II. Journal of Evolution Equations. Springer
Nature. https://doi.org/10.1007/s00028-022-00786-7
chicago: Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution
Equations in Critical Spaces Part II.” Journal of Evolution Equations.
Springer Nature, 2022. https://doi.org/10.1007/s00028-022-00786-7.
ieee: A. Agresti and M. Veraar, “Nonlinear parabolic stochastic evolution equations
in critical spaces part II,” Journal of Evolution Equations, vol. 22, no.
2. Springer Nature, 2022.
ista: Agresti A, Veraar M. 2022. Nonlinear parabolic stochastic evolution equations
in critical spaces part II. Journal of Evolution Equations. 22(2), 56.
mla: Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution
Equations in Critical Spaces Part II.” Journal of Evolution Equations,
vol. 22, no. 2, 56, Springer Nature, 2022, doi:10.1007/s00028-022-00786-7.
short: A. Agresti, M. Veraar, Journal of Evolution Equations 22 (2022).
date_created: 2022-08-16T08:39:43Z
date_published: 2022-06-01T00:00:00Z
date_updated: 2023-08-03T12:53:51Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00028-022-00786-7
external_id:
isi:
- '000809108500001'
file:
- access_level: open_access
checksum: 59b99d1b48b6bd40983e7ce298524a21
content_type: application/pdf
creator: kschuh
date_created: 2022-08-16T08:52:46Z
date_updated: 2022-08-16T08:52:46Z
file_id: '11862'
file_name: 2022_Journal of Evolution Equations_Agresti.pdf
file_size: 1758371
relation: main_file
success: 1
file_date_updated: 2022-08-16T08:52:46Z
has_accepted_license: '1'
intvolume: ' 22'
isi: 1
issue: '2'
keyword:
- Mathematics (miscellaneous)
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
publication: Journal of Evolution Equations
publication_identifier:
eissn:
- 1424-3202
issn:
- 1424-3199
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Nonlinear parabolic stochastic evolution equations in critical spaces part
II
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 22
year: '2022'
...
---
_id: '12079'
abstract:
- lang: eng
text: We extend the recent rigorous convergence result of Abels and Moser (SIAM
J Math Anal 54(1):114–172, 2022. https://doi.org/10.1137/21M1424925) concerning
convergence rates for solutions of the Allen–Cahn equation with a nonlinear Robin
boundary condition towards evolution by mean curvature flow with constant contact
angle. More precisely, in the present work we manage to remove the perturbative
assumption on the contact angle being close to 90∘. We establish under usual double-well
type assumptions on the potential and for a certain class of boundary energy densities
the sub-optimal convergence rate of order ε12 for general contact angles α∈(0,π).
For a very specific form of the boundary energy density, we even obtain from our
methods a sharp convergence rate of order ε; again for general contact angles
α∈(0,π). Our proof deviates from the popular strategy based on rigorous asymptotic
expansions and stability estimates for the linearized Allen–Cahn operator. Instead,
we follow the recent approach by Fischer et al. (SIAM J Math Anal 52(6):6222–6233,
2020. https://doi.org/10.1137/20M1322182), thus relying on a relative entropy
technique. We develop a careful adaptation of their approach in order to encode
the constant contact angle condition. In fact, we perform this task at the level
of the notion of gradient flow calibrations. This concept was recently introduced
in the context of weak-strong uniqueness for multiphase mean curvature flow by
Fischer et al. (arXiv:2003.05478v2).
acknowledgement: "This Project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(Grant Agreement No 948819) , and from the Deutsche Forschungsgemeinschaft (DFG,
German Research Foundation) under Germany’s Excellence Strategy—EXC-2047/1 - 390685813.\r\nOpen
Access funding enabled and organized by Projekt DEAL."
article_number: '201'
article_processing_charge: No
article_type: original
author:
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
- first_name: Maximilian
full_name: Moser, Maximilian
id: a60047a9-da77-11eb-85b4-c4dc385ebb8c
last_name: Moser
citation:
ama: 'Hensel S, Moser M. Convergence rates for the Allen–Cahn equation with boundary
contact energy: The non-perturbative regime. Calculus of Variations and Partial
Differential Equations. 2022;61(6). doi:10.1007/s00526-022-02307-3'
apa: 'Hensel, S., & Moser, M. (2022). Convergence rates for the Allen–Cahn equation
with boundary contact energy: The non-perturbative regime. Calculus of Variations
and Partial Differential Equations. Springer Nature. https://doi.org/10.1007/s00526-022-02307-3'
chicago: 'Hensel, Sebastian, and Maximilian Moser. “Convergence Rates for the Allen–Cahn
Equation with Boundary Contact Energy: The Non-Perturbative Regime.” Calculus
of Variations and Partial Differential Equations. Springer Nature, 2022. https://doi.org/10.1007/s00526-022-02307-3.'
ieee: 'S. Hensel and M. Moser, “Convergence rates for the Allen–Cahn equation with
boundary contact energy: The non-perturbative regime,” Calculus of Variations
and Partial Differential Equations, vol. 61, no. 6. Springer Nature, 2022.'
ista: 'Hensel S, Moser M. 2022. Convergence rates for the Allen–Cahn equation with
boundary contact energy: The non-perturbative regime. Calculus of Variations and
Partial Differential Equations. 61(6), 201.'
mla: 'Hensel, Sebastian, and Maximilian Moser. “Convergence Rates for the Allen–Cahn
Equation with Boundary Contact Energy: The Non-Perturbative Regime.” Calculus
of Variations and Partial Differential Equations, vol. 61, no. 6, 201, Springer
Nature, 2022, doi:10.1007/s00526-022-02307-3.'
short: S. Hensel, M. Moser, Calculus of Variations and Partial Differential Equations
61 (2022).
date_created: 2022-09-11T22:01:54Z
date_published: 2022-08-24T00:00:00Z
date_updated: 2023-08-03T13:48:30Z
day: '24'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00526-022-02307-3
ec_funded: 1
external_id:
isi:
- '000844247300008'
file:
- access_level: open_access
checksum: b2da020ce50440080feedabeab5b09c4
content_type: application/pdf
creator: dernst
date_created: 2023-01-20T08:56:01Z
date_updated: 2023-01-20T08:56:01Z
file_id: '12320'
file_name: 2022_Calculus_Hensel.pdf
file_size: 1278493
relation: main_file
success: 1
file_date_updated: 2023-01-20T08:56:01Z
has_accepted_license: '1'
intvolume: ' 61'
isi: 1
issue: '6'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Calculus of Variations and Partial Differential Equations
publication_identifier:
eissn:
- 1432-0835
issn:
- 0944-2669
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Convergence rates for the Allen–Cahn equation with boundary contact energy:
The non-perturbative regime'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 61
year: '2022'
...
---
_id: '12178'
abstract:
- lang: eng
text: In this paper we consider the stochastic primitive equation for geophysical
flows subject to transport noise and turbulent pressure. Admitting very rough
noise terms, the global existence and uniqueness of solutions to this stochastic
partial differential equation are proven using stochastic maximal L² regularity,
the theory of critical spaces for stochastic evolution equations, and global a
priori bounds. Compared to other results in this direction, we do not need any
smallness assumption on the transport noise which acts directly on the velocity
field and we also allow rougher noise terms. The adaptation to Stratonovich type
noise and, more generally, to variable viscosity and/or conductivity are discussed
as well.
acknowledgement: The authors thank the anonymous referees for their helpful comments
and suggestions. Open Access funding enabled and organized by Projekt DEAL.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Antonio
full_name: Agresti, Antonio
id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72
last_name: Agresti
orcid: 0000-0002-9573-2962
- first_name: Matthias
full_name: Hieber, Matthias
last_name: Hieber
- first_name: Amru
full_name: Hussein, Amru
last_name: Hussein
- first_name: Martin
full_name: Saal, Martin
last_name: Saal
citation:
ama: 'Agresti A, Hieber M, Hussein A, Saal M. The stochastic primitive equations
with transport noise and turbulent pressure. Stochastics and Partial Differential
Equations: Analysis and Computations. 2022. doi:10.1007/s40072-022-00277-3'
apa: 'Agresti, A., Hieber, M., Hussein, A., & Saal, M. (2022). The stochastic
primitive equations with transport noise and turbulent pressure. Stochastics
and Partial Differential Equations: Analysis and Computations. Springer Nature.
https://doi.org/10.1007/s40072-022-00277-3'
chicago: 'Agresti, Antonio, Matthias Hieber, Amru Hussein, and Martin Saal. “The
Stochastic Primitive Equations with Transport Noise and Turbulent Pressure.” Stochastics
and Partial Differential Equations: Analysis and Computations. Springer Nature,
2022. https://doi.org/10.1007/s40072-022-00277-3.'
ieee: 'A. Agresti, M. Hieber, A. Hussein, and M. Saal, “The stochastic primitive
equations with transport noise and turbulent pressure,” Stochastics and Partial
Differential Equations: Analysis and Computations. Springer Nature, 2022.'
ista: 'Agresti A, Hieber M, Hussein A, Saal M. 2022. The stochastic primitive equations
with transport noise and turbulent pressure. Stochastics and Partial Differential
Equations: Analysis and Computations.'
mla: 'Agresti, Antonio, et al. “The Stochastic Primitive Equations with Transport
Noise and Turbulent Pressure.” Stochastics and Partial Differential Equations:
Analysis and Computations, Springer Nature, 2022, doi:10.1007/s40072-022-00277-3.'
short: 'A. Agresti, M. Hieber, A. Hussein, M. Saal, Stochastics and Partial Differential
Equations: Analysis and Computations (2022).'
date_created: 2023-01-12T12:12:29Z
date_published: 2022-10-27T00:00:00Z
date_updated: 2023-08-16T09:11:38Z
day: '27'
department:
- _id: JuFi
doi: 10.1007/s40072-022-00277-3
external_id:
isi:
- '000874389000001'
isi: 1
keyword:
- Applied Mathematics
- Modeling and Simulation
- Statistics and Probability
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s40072-022-00277-3
month: '10'
oa: 1
oa_version: Published Version
publication: 'Stochastics and Partial Differential Equations: Analysis and Computations'
publication_identifier:
eissn:
- 2194-041X
issn:
- 2194-0401
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: The stochastic primitive equations with transport noise and turbulent pressure
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2022'
...
---
_id: '12304'
abstract:
- lang: eng
text: 'We establish sharp criteria for the instantaneous propagation of free boundaries
in solutions to the thin-film equation. The criteria are formulated in terms of
the initial distribution of mass (as opposed to previous almost-optimal results),
reflecting the fact that mass is a locally conserved quantity for the thin-film
equation. In the regime of weak slippage, our criteria are at the same time necessary
and sufficient. The proof of our upper bounds on free boundary propagation is
based on a strategy of “propagation of degeneracy” down to arbitrarily small spatial
scales: We combine estimates on the local mass and estimates on energies to show
that “degeneracy” on a certain space-time cylinder entails “degeneracy” on a spatially
smaller space-time cylinder with the same time horizon. The derivation of our
lower bounds on free boundary propagation is based on a combination of a monotone
quantity and almost optimal estimates established previously by the second author
with a new estimate connecting motion of mass to entropy production.'
acknowledgement: N. De Nitti acknowledges the kind hospitality of IST Austria within
the framework of the ISTernship Summer Program 2018, during which most of the present
article was written. N. DeNitti has received funding by The Austrian Agency for
International Cooperation in Education &Research (OeAD-GmbH) via its financial support
of the ISTernship Summer Program 2018. N.De Nitti would also like to thank Giuseppe
Coclite, Giuseppe Devillanova, Giuseppe Florio, Sebastian Hensel, and Francesco
Maddalena for several helpful conversations on topics related to this work.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nicola
full_name: De Nitti, Nicola
last_name: De Nitti
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
citation:
ama: De Nitti N, Fischer JL. Sharp criteria for the waiting time phenomenon in solutions
to the thin-film equation. Communications in Partial Differential Equations.
2022;47(7):1394-1434. doi:10.1080/03605302.2022.2056702
apa: De Nitti, N., & Fischer, J. L. (2022). Sharp criteria for the waiting time
phenomenon in solutions to the thin-film equation. Communications in Partial
Differential Equations. Taylor & Francis. https://doi.org/10.1080/03605302.2022.2056702
chicago: De Nitti, Nicola, and Julian L Fischer. “Sharp Criteria for the Waiting
Time Phenomenon in Solutions to the Thin-Film Equation.” Communications in
Partial Differential Equations. Taylor & Francis, 2022. https://doi.org/10.1080/03605302.2022.2056702.
ieee: N. De Nitti and J. L. Fischer, “Sharp criteria for the waiting time phenomenon
in solutions to the thin-film equation,” Communications in Partial Differential
Equations, vol. 47, no. 7. Taylor & Francis, pp. 1394–1434, 2022.
ista: De Nitti N, Fischer JL. 2022. Sharp criteria for the waiting time phenomenon
in solutions to the thin-film equation. Communications in Partial Differential
Equations. 47(7), 1394–1434.
mla: De Nitti, Nicola, and Julian L. Fischer. “Sharp Criteria for the Waiting Time
Phenomenon in Solutions to the Thin-Film Equation.” Communications in Partial
Differential Equations, vol. 47, no. 7, Taylor & Francis, 2022, pp. 1394–434,
doi:10.1080/03605302.2022.2056702.
short: N. De Nitti, J.L. Fischer, Communications in Partial Differential Equations
47 (2022) 1394–1434.
date_created: 2023-01-16T10:06:50Z
date_published: 2022-07-01T00:00:00Z
date_updated: 2023-08-04T10:34:31Z
day: '01'
department:
- _id: JuFi
doi: 10.1080/03605302.2022.2056702
external_id:
arxiv:
- '1907.05342'
isi:
- '000805689800001'
intvolume: ' 47'
isi: 1
issue: '7'
keyword:
- Applied Mathematics
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.1907.05342'
month: '07'
oa: 1
oa_version: Preprint
page: 1394-1434
publication: Communications in Partial Differential Equations
publication_identifier:
eissn:
- 1532-4133
issn:
- 0360-5302
publication_status: published
publisher: Taylor & Francis
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sharp criteria for the waiting time phenomenon in solutions to the thin-film
equation
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 47
year: '2022'
...
---
_id: '12305'
abstract:
- lang: eng
text: This paper is concerned with the sharp interface limit for the Allen--Cahn
equation with a nonlinear Robin boundary condition in a bounded smooth domain
Ω⊂\R2. We assume that a diffuse interface already has developed and that it is
in contact with the boundary ∂Ω. The boundary condition is designed in such a
way that the limit problem is given by the mean curvature flow with constant α-contact
angle. For α close to 90° we prove a local in time convergence result for well-prepared
initial data for times when a smooth solution to the limit problem exists. Based
on the latter we construct a suitable curvilinear coordinate system and carry
out a rigorous asymptotic expansion for the Allen--Cahn equation with the nonlinear
Robin boundary condition. Moreover, we show a spectral estimate for the corresponding
linearized Allen--Cahn operator and with its aid we derive strong norm estimates
for the difference of the exact and approximate solutions using a Gronwall-type
argument.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Helmut
full_name: Abels, Helmut
last_name: Abels
- first_name: Maximilian
full_name: Moser, Maximilian
id: a60047a9-da77-11eb-85b4-c4dc385ebb8c
last_name: Moser
citation:
ama: Abels H, Moser M. Convergence of the Allen--Cahn equation with a nonlinear
Robin boundary condition to mean curvature flow with contact angle close to 90°.
SIAM Journal on Mathematical Analysis. 2022;54(1):114-172. doi:10.1137/21m1424925
apa: Abels, H., & Moser, M. (2022). Convergence of the Allen--Cahn equation
with a nonlinear Robin boundary condition to mean curvature flow with contact
angle close to 90°. SIAM Journal on Mathematical Analysis. Society for
Industrial and Applied Mathematics. https://doi.org/10.1137/21m1424925
chicago: Abels, Helmut, and Maximilian Moser. “Convergence of the Allen--Cahn Equation
with a Nonlinear Robin Boundary Condition to Mean Curvature Flow with Contact
Angle Close to 90°.” SIAM Journal on Mathematical Analysis. Society for
Industrial and Applied Mathematics, 2022. https://doi.org/10.1137/21m1424925.
ieee: H. Abels and M. Moser, “Convergence of the Allen--Cahn equation with a nonlinear
Robin boundary condition to mean curvature flow with contact angle close to 90°,”
SIAM Journal on Mathematical Analysis, vol. 54, no. 1. Society for Industrial
and Applied Mathematics, pp. 114–172, 2022.
ista: Abels H, Moser M. 2022. Convergence of the Allen--Cahn equation with a nonlinear
Robin boundary condition to mean curvature flow with contact angle close to 90°.
SIAM Journal on Mathematical Analysis. 54(1), 114–172.
mla: Abels, Helmut, and Maximilian Moser. “Convergence of the Allen--Cahn Equation
with a Nonlinear Robin Boundary Condition to Mean Curvature Flow with Contact
Angle Close to 90°.” SIAM Journal on Mathematical Analysis, vol. 54, no.
1, Society for Industrial and Applied Mathematics, 2022, pp. 114–72, doi:10.1137/21m1424925.
short: H. Abels, M. Moser, SIAM Journal on Mathematical Analysis 54 (2022) 114–172.
date_created: 2023-01-16T10:07:00Z
date_published: 2022-01-04T00:00:00Z
date_updated: 2023-08-04T10:34:56Z
day: '04'
department:
- _id: JuFi
doi: 10.1137/21m1424925
external_id:
arxiv:
- '2105.08434'
isi:
- '000762768000004'
intvolume: ' 54'
isi: 1
issue: '1'
keyword:
- Applied Mathematics
- Computational Mathematics
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2105.08434'
month: '01'
oa: 1
oa_version: Preprint
page: 114-172
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
eissn:
- 1095-7154
issn:
- 0036-1410
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition
to mean curvature flow with contact angle close to 90°
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 54
year: '2022'
...
---
_id: '8792'
abstract:
- lang: eng
text: This paper is concerned with a non-isothermal Cahn-Hilliard model based on
a microforce balance. The model was derived by A. Miranville and G. Schimperna
starting from the two fundamental laws of Thermodynamics, following M. Gurtin's
two-scale approach. The main working assumptions are made on the behaviour of
the heat flux as the absolute temperature tends to zero and to infinity. A suitable
Ginzburg-Landau free energy is considered. Global-in-time existence for the initial-boundary
value problem associated to the entropy formulation and, in a subcase, also to
the weak formulation of the model is proved by deriving suitable a priori estimates
and by showing weak sequential stability of families of approximating solutions.
At last, some highlights are given regarding a possible approximation scheme compatible
with the a-priori estimates available for the system.
acknowledgement: G. Schimperna has been partially supported by GNAMPA (Gruppo Nazionale
per l'Analisi Matematica, la Probabilità e le loro Applicazioni) of INdAM (Istituto
Nazionale di Alta Matematica).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Alice
full_name: Marveggio, Alice
id: 25647992-AA84-11E9-9D75-8427E6697425
last_name: Marveggio
- first_name: Giulio
full_name: Schimperna, Giulio
last_name: Schimperna
citation:
ama: Marveggio A, Schimperna G. On a non-isothermal Cahn-Hilliard model based on
a microforce balance. Journal of Differential Equations. 2021;274(2):924-970.
doi:10.1016/j.jde.2020.10.030
apa: Marveggio, A., & Schimperna, G. (2021). On a non-isothermal Cahn-Hilliard
model based on a microforce balance. Journal of Differential Equations.
Elsevier. https://doi.org/10.1016/j.jde.2020.10.030
chicago: Marveggio, Alice, and Giulio Schimperna. “On a Non-Isothermal Cahn-Hilliard
Model Based on a Microforce Balance.” Journal of Differential Equations.
Elsevier, 2021. https://doi.org/10.1016/j.jde.2020.10.030.
ieee: A. Marveggio and G. Schimperna, “On a non-isothermal Cahn-Hilliard model based
on a microforce balance,” Journal of Differential Equations, vol. 274,
no. 2. Elsevier, pp. 924–970, 2021.
ista: Marveggio A, Schimperna G. 2021. On a non-isothermal Cahn-Hilliard model based
on a microforce balance. Journal of Differential Equations. 274(2), 924–970.
mla: Marveggio, Alice, and Giulio Schimperna. “On a Non-Isothermal Cahn-Hilliard
Model Based on a Microforce Balance.” Journal of Differential Equations,
vol. 274, no. 2, Elsevier, 2021, pp. 924–70, doi:10.1016/j.jde.2020.10.030.
short: A. Marveggio, G. Schimperna, Journal of Differential Equations 274 (2021)
924–970.
date_created: 2020-11-22T23:01:26Z
date_published: 2021-02-15T00:00:00Z
date_updated: 2023-08-04T11:12:16Z
day: '15'
department:
- _id: JuFi
doi: 10.1016/j.jde.2020.10.030
external_id:
arxiv:
- '2004.02618'
isi:
- '000600845300023'
intvolume: ' 274'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2004.02618
month: '02'
oa: 1
oa_version: Preprint
page: 924-970
publication: Journal of Differential Equations
publication_identifier:
eissn:
- '10902732'
issn:
- '00220396'
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: On a non-isothermal Cahn-Hilliard model based on a microforce balance
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 274
year: '2021'
...
---
_id: '9240'
abstract:
- lang: eng
text: A stochastic PDE, describing mesoscopic fluctuations in systems of weakly
interacting inertial particles of finite volume, is proposed and analysed in any
finite dimension . It is a regularised and inertial version of the Dean–Kawasaki
model. A high-probability well-posedness theory for this model is developed. This
theory improves significantly on the spatial scaling restrictions imposed in an
earlier work of the same authors, which applied only to significantly larger particles
in one dimension. The well-posedness theory now applies in d-dimensions when the
particle-width ϵ is proportional to for and N is the number of particles. This
scaling is optimal in a certain Sobolev norm. Key tools of the analysis are fractional
Sobolev spaces, sharp bounds on Bessel functions, separability of the regularisation
in the d-spatial dimensions, and use of the Faà di Bruno's formula.
acknowledgement: All authors thank the anonymous referee for his/her careful reading
of the manuscript and valuable suggestions. This paper was motivated by stimulating
discussions at the First Berlin–Leipzig Workshop on Fluctuating Hydrodynamics in
August 2019 with Ana Djurdjevac, Rupert Klein and Ralf Kornhuber. JZ gratefully
acknowledges funding by a Royal Society Wolfson Research Merit Award. FC gratefully
acknowledges funding from the European Union’s Horizon 2020 research and innovation
programme under the Marie Skłodowska-Curie grant agreement No. 754411.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Federico
full_name: Cornalba, Federico
id: 2CEB641C-A400-11E9-A717-D712E6697425
last_name: Cornalba
- first_name: Tony
full_name: Shardlow, Tony
last_name: Shardlow
- first_name: Johannes
full_name: Zimmer, Johannes
last_name: Zimmer
citation:
ama: Cornalba F, Shardlow T, Zimmer J. Well-posedness for a regularised inertial
Dean–Kawasaki model for slender particles in several space dimensions. Journal
of Differential Equations. 2021;284(5):253-283. doi:10.1016/j.jde.2021.02.048
apa: Cornalba, F., Shardlow, T., & Zimmer, J. (2021). Well-posedness for a regularised
inertial Dean–Kawasaki model for slender particles in several space dimensions.
Journal of Differential Equations. Elsevier. https://doi.org/10.1016/j.jde.2021.02.048
chicago: Cornalba, Federico, Tony Shardlow, and Johannes Zimmer. “Well-Posedness
for a Regularised Inertial Dean–Kawasaki Model for Slender Particles in Several
Space Dimensions.” Journal of Differential Equations. Elsevier, 2021. https://doi.org/10.1016/j.jde.2021.02.048.
ieee: F. Cornalba, T. Shardlow, and J. Zimmer, “Well-posedness for a regularised
inertial Dean–Kawasaki model for slender particles in several space dimensions,”
Journal of Differential Equations, vol. 284, no. 5. Elsevier, pp. 253–283,
2021.
ista: Cornalba F, Shardlow T, Zimmer J. 2021. Well-posedness for a regularised inertial
Dean–Kawasaki model for slender particles in several space dimensions. Journal
of Differential Equations. 284(5), 253–283.
mla: Cornalba, Federico, et al. “Well-Posedness for a Regularised Inertial Dean–Kawasaki
Model for Slender Particles in Several Space Dimensions.” Journal of Differential
Equations, vol. 284, no. 5, Elsevier, 2021, pp. 253–83, doi:10.1016/j.jde.2021.02.048.
short: F. Cornalba, T. Shardlow, J. Zimmer, Journal of Differential Equations 284
(2021) 253–283.
date_created: 2021-03-14T23:01:32Z
date_published: 2021-05-25T00:00:00Z
date_updated: 2023-08-07T14:08:05Z
day: '25'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1016/j.jde.2021.02.048
ec_funded: 1
external_id:
isi:
- '000634823300010'
file:
- access_level: open_access
checksum: c630b691fb9e716b02aa6103a9794ec8
content_type: application/pdf
creator: dernst
date_created: 2021-03-22T07:18:01Z
date_updated: 2021-03-22T07:18:01Z
file_id: '9267'
file_name: 2021_JourDiffEquations_Cornalba.pdf
file_size: 473310
relation: main_file
success: 1
file_date_updated: 2021-03-22T07:18:01Z
has_accepted_license: '1'
intvolume: ' 284'
isi: 1
issue: '5'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 253-283
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Journal of Differential Equations
publication_identifier:
eissn:
- 1090-2732
issn:
- 0022-0396
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Well-posedness for a regularised inertial Dean–Kawasaki model for slender particles
in several space dimensions
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 284
year: '2021'
...
---
_id: '9307'
abstract:
- lang: eng
text: We establish finite time extinction with probability one for weak solutions
of the Cauchy–Dirichlet problem for the 1D stochastic porous medium equation with
Stratonovich transport noise and compactly supported smooth initial datum. Heuristically,
this is expected to hold because Brownian motion has average spread rate O(t12)
whereas the support of solutions to the deterministic PME grows only with rate
O(t1m+1). The rigorous proof relies on a contraction principle up to time-dependent
shift for Wong–Zakai type approximations, the transformation to a deterministic
PME with two copies of a Brownian path as the lateral boundary, and techniques
from the theory of viscosity solutions.
acknowledgement: This project has received funding from the European Union’s Horizon
2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement
No. 665385 . I am very grateful to M. Gerencsér and J. Maas for proposing this problem
as well as helpful discussions. Special thanks go to F. Cornalba for suggesting
the additional κ-truncation in Proposition 5. I am also indebted to an anonymous
referee for pointing out a gap in a previous version of the proof of Lemma 9 (concerning
the treatment of the noise term). The issue is resolved in this version.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
citation:
ama: 'Hensel S. Finite time extinction for the 1D stochastic porous medium equation
with transport noise. Stochastics and Partial Differential Equations: Analysis
and Computations. 2021;9:892–939. doi:10.1007/s40072-021-00188-9'
apa: 'Hensel, S. (2021). Finite time extinction for the 1D stochastic porous medium
equation with transport noise. Stochastics and Partial Differential Equations:
Analysis and Computations. Springer Nature. https://doi.org/10.1007/s40072-021-00188-9'
chicago: 'Hensel, Sebastian. “Finite Time Extinction for the 1D Stochastic Porous
Medium Equation with Transport Noise.” Stochastics and Partial Differential
Equations: Analysis and Computations. Springer Nature, 2021. https://doi.org/10.1007/s40072-021-00188-9.'
ieee: 'S. Hensel, “Finite time extinction for the 1D stochastic porous medium equation
with transport noise,” Stochastics and Partial Differential Equations: Analysis
and Computations, vol. 9. Springer Nature, pp. 892–939, 2021.'
ista: 'Hensel S. 2021. Finite time extinction for the 1D stochastic porous medium
equation with transport noise. Stochastics and Partial Differential Equations:
Analysis and Computations. 9, 892–939.'
mla: 'Hensel, Sebastian. “Finite Time Extinction for the 1D Stochastic Porous Medium
Equation with Transport Noise.” Stochastics and Partial Differential Equations:
Analysis and Computations, vol. 9, Springer Nature, 2021, pp. 892–939, doi:10.1007/s40072-021-00188-9.'
short: 'S. Hensel, Stochastics and Partial Differential Equations: Analysis and
Computations 9 (2021) 892–939.'
date_created: 2021-04-04T22:01:21Z
date_published: 2021-03-21T00:00:00Z
date_updated: 2023-08-07T14:31:59Z
day: '21'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s40072-021-00188-9
ec_funded: 1
external_id:
isi:
- '000631001700001'
file:
- access_level: open_access
checksum: 6529b609c9209861720ffa4685111bc6
content_type: application/pdf
creator: dernst
date_created: 2021-04-06T09:31:28Z
date_updated: 2021-04-06T09:31:28Z
file_id: '9309'
file_name: 2021_StochPartDiffEquation_Hensel.pdf
file_size: 727005
relation: main_file
success: 1
file_date_updated: 2021-04-06T09:31:28Z
has_accepted_license: '1'
intvolume: ' 9'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 892–939
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: 'Stochastics and Partial Differential Equations: Analysis and Computations'
publication_identifier:
eissn:
- 2194-041X
issn:
- 2194-0401
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Finite time extinction for the 1D stochastic porous medium equation with transport
noise
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 9
year: '2021'
...
---
_id: '9335'
abstract:
- lang: eng
text: 'Various degenerate diffusion equations exhibit a waiting time phenomenon:
depending on the “flatness” of the compactly supported initial datum at the boundary
of the support, the support of the solution may not expand for a certain amount
of time. We show that this phenomenon is captured by particular Lagrangian discretizations
of the porous medium and the thin film equations, and we obtain sufficient criteria
for the occurrence of waiting times that are consistent with the known ones for
the original PDEs. For the spatially discrete solution, the waiting time phenomenon
refers to a deviation of the edge of support from its original position by a quantity
comparable to the mesh width, over a mesh-independent time interval. Our proof
is based on estimates on the fluid velocity in Lagrangian coordinates. Combining
weighted entropy estimates with an iteration technique à la Stampacchia leads
to upper bounds on free boundary propagation. Numerical simulations show that
the phenomenon is already clearly visible for relatively coarse discretizations.'
acknowledgement: This research was supported by the DFG Collaborative Research Center
TRR 109, “Discretization in Geometry and Dynamics”.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Daniel
full_name: Matthes, Daniel
last_name: Matthes
citation:
ama: Fischer JL, Matthes D. The waiting time phenomenon in spatially discretized
porous medium and thin film equations. SIAM Journal on Numerical Analysis.
2021;59(1):60-87. doi:10.1137/19M1300017
apa: Fischer, J. L., & Matthes, D. (2021). The waiting time phenomenon in spatially
discretized porous medium and thin film equations. SIAM Journal on Numerical
Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/19M1300017
chicago: Fischer, Julian L, and Daniel Matthes. “The Waiting Time Phenomenon in
Spatially Discretized Porous Medium and Thin Film Equations.” SIAM Journal
on Numerical Analysis. Society for Industrial and Applied Mathematics, 2021.
https://doi.org/10.1137/19M1300017.
ieee: J. L. Fischer and D. Matthes, “The waiting time phenomenon in spatially discretized
porous medium and thin film equations,” SIAM Journal on Numerical Analysis,
vol. 59, no. 1. Society for Industrial and Applied Mathematics, pp. 60–87, 2021.
ista: Fischer JL, Matthes D. 2021. The waiting time phenomenon in spatially discretized
porous medium and thin film equations. SIAM Journal on Numerical Analysis. 59(1),
60–87.
mla: Fischer, Julian L., and Daniel Matthes. “The Waiting Time Phenomenon in Spatially
Discretized Porous Medium and Thin Film Equations.” SIAM Journal on Numerical
Analysis, vol. 59, no. 1, Society for Industrial and Applied Mathematics,
2021, pp. 60–87, doi:10.1137/19M1300017.
short: J.L. Fischer, D. Matthes, SIAM Journal on Numerical Analysis 59 (2021) 60–87.
date_created: 2021-04-18T22:01:42Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2023-08-08T13:10:40Z
day: '01'
department:
- _id: JuFi
doi: 10.1137/19M1300017
external_id:
arxiv:
- '1911.04185'
isi:
- '000625044600003'
intvolume: ' 59'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1911.04185
month: '01'
oa: 1
oa_version: Preprint
page: 60-87
publication: SIAM Journal on Numerical Analysis
publication_identifier:
issn:
- 0036-1429
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: The waiting time phenomenon in spatially discretized porous medium and thin
film equations
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 59
year: '2021'
...
---
_id: '9352'
abstract:
- lang: eng
text: This paper provides an a priori error analysis of a localized orthogonal decomposition
method for the numerical stochastic homogenization of a model random diffusion
problem. If the uniformly elliptic and bounded random coefficient field of the
model problem is stationary and satisfies a quantitative decorrelation assumption
in the form of the spectral gap inequality, then the expected $L^2$ error of the
method can be estimated, up to logarithmic factors, by $H+(\varepsilon/H)^{d/2}$,
$\varepsilon$ being the small correlation length of the random coefficient and
$H$ the width of the coarse finite element mesh that determines the spatial resolution.
The proof bridges recent results of numerical homogenization and quantitative
stochastic homogenization.
acknowledgement: 'This work was initiated while the authors enjoyed the kind hospitality
of the Hausdorff Institute for Mathematics in Bonn during the trimester program
Multiscale Problems: Algorithms, Numerical Analysis, and Computation. D. Peterseim
would like to acknowledge the kind hospitality of the Erwin Schrödinger International
Institute for Mathematics and Physics (ESI), where parts of this research were
developed under the frame of the thematic program Numerical Analysis of Complex
PDE Models in the Sciences.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Dietmar
full_name: Gallistl, Dietmar
last_name: Gallistl
- first_name: Dietmar
full_name: Peterseim, Dietmar
last_name: Peterseim
citation:
ama: Fischer JL, Gallistl D, Peterseim D. A priori error analysis of a numerical
stochastic homogenization method. SIAM Journal on Numerical Analysis. 2021;59(2):660-674.
doi:10.1137/19M1308992
apa: Fischer, J. L., Gallistl, D., & Peterseim, D. (2021). A priori error analysis
of a numerical stochastic homogenization method. SIAM Journal on Numerical
Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/19M1308992
chicago: Fischer, Julian L, Dietmar Gallistl, and Dietmar Peterseim. “A Priori Error
Analysis of a Numerical Stochastic Homogenization Method.” SIAM Journal on
Numerical Analysis. Society for Industrial and Applied Mathematics, 2021.
https://doi.org/10.1137/19M1308992.
ieee: J. L. Fischer, D. Gallistl, and D. Peterseim, “A priori error analysis of
a numerical stochastic homogenization method,” SIAM Journal on Numerical Analysis,
vol. 59, no. 2. Society for Industrial and Applied Mathematics, pp. 660–674, 2021.
ista: Fischer JL, Gallistl D, Peterseim D. 2021. A priori error analysis of a numerical
stochastic homogenization method. SIAM Journal on Numerical Analysis. 59(2), 660–674.
mla: Fischer, Julian L., et al. “A Priori Error Analysis of a Numerical Stochastic
Homogenization Method.” SIAM Journal on Numerical Analysis, vol. 59, no.
2, Society for Industrial and Applied Mathematics, 2021, pp. 660–74, doi:10.1137/19M1308992.
short: J.L. Fischer, D. Gallistl, D. Peterseim, SIAM Journal on Numerical Analysis
59 (2021) 660–674.
date_created: 2021-04-25T22:01:31Z
date_published: 2021-03-09T00:00:00Z
date_updated: 2023-08-08T13:13:37Z
day: '09'
department:
- _id: JuFi
doi: 10.1137/19M1308992
external_id:
arxiv:
- '1912.11646'
isi:
- '000646030400003'
intvolume: ' 59'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1912.11646
month: '03'
oa: 1
oa_version: Preprint
page: 660-674
publication: SIAM Journal on Numerical Analysis
publication_identifier:
issn:
- 0036-1429
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: A priori error analysis of a numerical stochastic homogenization method
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 59
year: '2021'
...
---
_id: '10005'
abstract:
- lang: eng
text: We study systems of nonlinear partial differential equations of parabolic
type, in which the elliptic operator is replaced by the first-order divergence
operator acting on a flux function, which is related to the spatial gradient of
the unknown through an additional implicit equation. This setting, broad enough
in terms of applications, significantly expands the paradigm of nonlinear parabolic
problems. Formulating four conditions concerning the form of the implicit equation,
we first show that these conditions describe a maximal monotone p-coercive graph.
We then establish the global-in-time and large-data existence of a (weak) solution
and its uniqueness. To this end, we adopt and significantly generalize Minty’s
method of monotone mappings. A unified theory, containing several novel tools,
is developed in a way to be tractable from the point of view of numerical approximations.
acknowledgement: "M. Bulíček and J. Málek acknowledge the support of the project No.
18-12719S financed by the Czech\r\nScience foundation (GAČR). E. Maringová acknowledges
support from Charles University Research program \r\nUNCE/SCI/023, the grant SVV-2020-260583
by the Ministry of Education, Youth and Sports, Czech Republic\r\nand from the Austrian
Science Fund (FWF), grants P30000, W1245, and F65. M. Bulíček and J. Málek are\r\nmembers
of the Nečas Center for Mathematical Modelling.\r\n"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Miroslav
full_name: Bulíček, Miroslav
last_name: Bulíček
- first_name: Erika
full_name: Maringová, Erika
id: dbabca31-66eb-11eb-963a-fb9c22c880b4
last_name: Maringová
- first_name: Josef
full_name: Málek, Josef
last_name: Málek
citation:
ama: Bulíček M, Maringová E, Málek J. On nonlinear problems of parabolic type with
implicit constitutive equations involving flux. Mathematical Models and Methods
in Applied Sciences. 2021;31(09). doi:10.1142/S0218202521500457
apa: Bulíček, M., Maringová, E., & Málek, J. (2021). On nonlinear problems of
parabolic type with implicit constitutive equations involving flux. Mathematical
Models and Methods in Applied Sciences. World Scientific. https://doi.org/10.1142/S0218202521500457
chicago: Bulíček, Miroslav, Erika Maringová, and Josef Málek. “On Nonlinear Problems
of Parabolic Type with Implicit Constitutive Equations Involving Flux.” Mathematical
Models and Methods in Applied Sciences. World Scientific, 2021. https://doi.org/10.1142/S0218202521500457.
ieee: M. Bulíček, E. Maringová, and J. Málek, “On nonlinear problems of parabolic
type with implicit constitutive equations involving flux,” Mathematical Models
and Methods in Applied Sciences, vol. 31, no. 09. World Scientific, 2021.
ista: Bulíček M, Maringová E, Málek J. 2021. On nonlinear problems of parabolic
type with implicit constitutive equations involving flux. Mathematical Models
and Methods in Applied Sciences. 31(09).
mla: Bulíček, Miroslav, et al. “On Nonlinear Problems of Parabolic Type with Implicit
Constitutive Equations Involving Flux.” Mathematical Models and Methods in
Applied Sciences, vol. 31, no. 09, World Scientific, 2021, doi:10.1142/S0218202521500457.
short: M. Bulíček, E. Maringová, J. Málek, Mathematical Models and Methods in Applied
Sciences 31 (2021).
date_created: 2021-09-12T22:01:25Z
date_published: 2021-08-25T00:00:00Z
date_updated: 2023-09-04T11:43:45Z
day: '25'
department:
- _id: JuFi
doi: 10.1142/S0218202521500457
external_id:
arxiv:
- '2009.06917'
isi:
- '000722222900004'
intvolume: ' 31'
isi: 1
issue: '09'
keyword:
- Nonlinear parabolic systems
- implicit constitutive theory
- weak solutions
- existence
- uniqueness
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2009.06917
month: '08'
oa: 1
oa_version: Preprint
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Mathematical Models and Methods in Applied Sciences
publication_identifier:
eissn:
- 1793-6314
issn:
- 0218-2025
publication_status: published
publisher: World Scientific
quality_controlled: '1'
scopus_import: '1'
status: public
title: On nonlinear problems of parabolic type with implicit constitutive equations
involving flux
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 31
year: '2021'
...
---
_id: '10007'
abstract:
- lang: eng
text: The present thesis is concerned with the derivation of weak-strong uniqueness
principles for curvature driven interface evolution problems not satisfying a
comparison principle. The specific examples being treated are two-phase Navier-Stokes
flow with surface tension, modeling the evolution of two incompressible, viscous
and immiscible fluids separated by a sharp interface, and multiphase mean curvature
flow, which serves as an idealized model for the motion of grain boundaries in
an annealing polycrystalline material. Our main results - obtained in joint works
with Julian Fischer, Tim Laux and Theresa M. Simon - state that prior to the formation
of geometric singularities due to topology changes, the weak solution concept
of Abels (Interfaces Free Bound. 9, 2007) to two-phase Navier-Stokes flow with
surface tension and the weak solution concept of Laux and Otto (Calc. Var. Partial
Differential Equations 55, 2016) to multiphase mean curvature flow (for networks
in R^2 or double bubbles in R^3) represents the unique solution to these interface
evolution problems within the class of classical solutions, respectively. To the
best of the author's knowledge, for interface evolution problems not admitting
a geometric comparison principle the derivation of a weak-strong uniqueness principle
represented an open problem, so that the works contained in the present thesis
constitute the first positive results in this direction. The key ingredient of
our approach consists of the introduction of a novel concept of relative entropies
for a class of curvature driven interface evolution problems, for which the associated
energy contains an interfacial contribution being proportional to the surface
area of the evolving (network of) interface(s). The interfacial part of the relative
entropy gives sufficient control on the interface error between a weak and a classical
solution, and its time evolution can be computed, at least in principle, for any
energy dissipating weak solution concept. A resulting stability estimate for the
relative entropy essentially entails the above mentioned weak-strong uniqueness
principles. The present thesis contains a detailed introduction to our relative
entropy approach, which in particular highlights potential applications to other
problems in curvature driven interface evolution not treated in this thesis.
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
citation:
ama: 'Hensel S. Curvature driven interface evolution: Uniqueness properties of weak
solution concepts. 2021. doi:10.15479/at:ista:10007'
apa: 'Hensel, S. (2021). Curvature driven interface evolution: Uniqueness properties
of weak solution concepts. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:10007'
chicago: 'Hensel, Sebastian. “Curvature Driven Interface Evolution: Uniqueness Properties
of Weak Solution Concepts.” Institute of Science and Technology Austria, 2021.
https://doi.org/10.15479/at:ista:10007.'
ieee: 'S. Hensel, “Curvature driven interface evolution: Uniqueness properties of
weak solution concepts,” Institute of Science and Technology Austria, 2021.'
ista: 'Hensel S. 2021. Curvature driven interface evolution: Uniqueness properties
of weak solution concepts. Institute of Science and Technology Austria.'
mla: 'Hensel, Sebastian. Curvature Driven Interface Evolution: Uniqueness Properties
of Weak Solution Concepts. Institute of Science and Technology Austria, 2021,
doi:10.15479/at:ista:10007.'
short: 'S. Hensel, Curvature Driven Interface Evolution: Uniqueness Properties of
Weak Solution Concepts, Institute of Science and Technology Austria, 2021.'
date_created: 2021-09-13T11:12:34Z
date_published: 2021-09-14T00:00:00Z
date_updated: 2023-09-07T13:30:45Z
day: '14'
ddc:
- '515'
degree_awarded: PhD
department:
- _id: GradSch
- _id: JuFi
doi: 10.15479/at:ista:10007
ec_funded: 1
file:
- access_level: closed
checksum: c8475faaf0b680b4971f638f1db16347
content_type: application/x-zip-compressed
creator: shensel
date_created: 2021-09-13T11:03:24Z
date_updated: 2021-09-15T14:37:30Z
file_id: '10008'
file_name: thesis_final_Hensel.zip
file_size: 15022154
relation: source_file
- access_level: open_access
checksum: 1a609937aa5275452822f45f2da17f07
content_type: application/pdf
creator: shensel
date_created: 2021-09-13T14:18:56Z
date_updated: 2021-09-14T09:52:47Z
file_id: '10014'
file_name: thesis_final_Hensel.pdf
file_size: 6583638
relation: main_file
file_date_updated: 2021-09-15T14:37:30Z
has_accepted_license: '1'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: '300'
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '10012'
relation: part_of_dissertation
status: public
- id: '10013'
relation: part_of_dissertation
status: public
- id: '7489'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
title: 'Curvature driven interface evolution: Uniqueness properties of weak solution
concepts'
type: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2021'
...
---
_id: '10011'
abstract:
- lang: eng
text: We propose a new weak solution concept for (two-phase) mean curvature flow
which enjoys both (unconditional) existence and (weak-strong) uniqueness properties.
These solutions are evolving varifolds, just as in Brakke's formulation, but are
coupled to the phase volumes by a simple transport equation. First, we show that,
in the exact same setup as in Ilmanen's proof [J. Differential Geom. 38, 417-461,
(1993)], any limit point of solutions to the Allen-Cahn equation is a varifold
solution in our sense. Second, we prove that any calibrated flow in the sense
of Fischer et al. [arXiv:2003.05478] - and hence any classical solution to mean
curvature flow - is unique in the class of our new varifold solutions. This is
in sharp contrast to the case of Brakke flows, which a priori may disappear at
any given time and are therefore fatally non-unique. Finally, we propose an extension
of the solution concept to the multi-phase case which is at least guaranteed to
satisfy a weak-strong uniqueness principle.
acknowledgement: This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No 948819), and from the Deutsche Forschungsgemeinschaft (DFG,
German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813.
The content of this paper was developed and parts of it were written during a visit
of the first author to the Hausdorff Center of Mathematics (HCM), University of
Bonn. The hospitality and the support of HCM are gratefully acknowledged.
article_number: '2109.04233'
article_processing_charge: No
arxiv: 1
author:
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
- first_name: Tim
full_name: Laux, Tim
last_name: Laux
citation:
ama: 'Hensel S, Laux T. A new varifold solution concept for mean curvature flow:
Convergence of the Allen-Cahn equation and weak-strong uniqueness. arXiv.
doi:10.48550/arXiv.2109.04233'
apa: 'Hensel, S., & Laux, T. (n.d.). A new varifold solution concept for mean
curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness.
arXiv. https://doi.org/10.48550/arXiv.2109.04233'
chicago: 'Hensel, Sebastian, and Tim Laux. “A New Varifold Solution Concept for
Mean Curvature Flow: Convergence of the Allen-Cahn Equation and Weak-Strong Uniqueness.”
ArXiv, n.d. https://doi.org/10.48550/arXiv.2109.04233.'
ieee: 'S. Hensel and T. Laux, “A new varifold solution concept for mean curvature
flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness,” arXiv.
.'
ista: 'Hensel S, Laux T. A new varifold solution concept for mean curvature flow:
Convergence of the Allen-Cahn equation and weak-strong uniqueness. arXiv, 2109.04233.'
mla: 'Hensel, Sebastian, and Tim Laux. “A New Varifold Solution Concept for Mean
Curvature Flow: Convergence of the Allen-Cahn Equation and Weak-Strong Uniqueness.”
ArXiv, 2109.04233, doi:10.48550/arXiv.2109.04233.'
short: S. Hensel, T. Laux, ArXiv (n.d.).
date_created: 2021-09-13T12:17:10Z
date_published: 2021-09-09T00:00:00Z
date_updated: 2023-05-03T10:34:38Z
day: '09'
department:
- _id: JuFi
doi: 10.48550/arXiv.2109.04233
ec_funded: 1
external_id:
arxiv:
- '2109.04233'
keyword:
- Mean curvature flow
- gradient flows
- varifolds
- weak solutions
- weak-strong uniqueness
- calibrated geometry
- gradient-flow calibrations
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2109.04233
month: '09'
oa: 1
oa_version: Preprint
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: arXiv
publication_status: submitted
status: public
title: 'A new varifold solution concept for mean curvature flow: Convergence of the
Allen-Cahn equation and weak-strong uniqueness'
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '10013'
abstract:
- lang: eng
text: We derive a weak-strong uniqueness principle for BV solutions to multiphase
mean curvature flow of triple line clusters in three dimensions. Our proof is
based on the explicit construction of a gradient-flow calibration in the sense
of the recent work of Fischer et al. [arXiv:2003.05478] for any such cluster.
This extends the two-dimensional construction to the three-dimensional case of
surfaces meeting along triple junctions.
acknowledgement: This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No 948819), and from the Deutsche Forschungsgemeinschaft (DFG,
German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813.
article_number: '2108.01733'
article_processing_charge: No
arxiv: 1
author:
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
- first_name: Tim
full_name: Laux, Tim
last_name: Laux
citation:
ama: Hensel S, Laux T. Weak-strong uniqueness for the mean curvature flow of double
bubbles. arXiv. doi:10.48550/arXiv.2108.01733
apa: Hensel, S., & Laux, T. (n.d.). Weak-strong uniqueness for the mean curvature
flow of double bubbles. arXiv. https://doi.org/10.48550/arXiv.2108.01733
chicago: Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature
Flow of Double Bubbles.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2108.01733.
ieee: S. Hensel and T. Laux, “Weak-strong uniqueness for the mean curvature flow
of double bubbles,” arXiv. .
ista: Hensel S, Laux T. Weak-strong uniqueness for the mean curvature flow of double
bubbles. arXiv, 2108.01733.
mla: Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature
Flow of Double Bubbles.” ArXiv, 2108.01733, doi:10.48550/arXiv.2108.01733.
short: S. Hensel, T. Laux, ArXiv (n.d.).
date_created: 2021-09-13T12:17:11Z
date_published: 2021-08-03T00:00:00Z
date_updated: 2023-09-07T13:30:45Z
day: '03'
department:
- _id: JuFi
doi: 10.48550/arXiv.2108.01733
ec_funded: 1
external_id:
arxiv:
- '2108.01733'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2108.01733
month: '08'
oa: 1
oa_version: Preprint
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: arXiv
publication_status: submitted
related_material:
record:
- id: '13043'
relation: later_version
status: public
- id: '10007'
relation: dissertation_contains
status: public
status: public
title: Weak-strong uniqueness for the mean curvature flow of double bubbles
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '10174'
abstract:
- lang: eng
text: Quantitative stochastic homogenization of linear elliptic operators is by
now well-understood. In this contribution we move forward to the nonlinear setting
of monotone operators with p-growth. This first work is dedicated to a quantitative
two-scale expansion result. Fluctuations will be addressed in companion articles.
By treating the range of exponents 2≤p<∞ in dimensions d≤3, we are able to consider
genuinely nonlinear elliptic equations and systems such as −∇⋅A(x)(1+|∇u|p−2)∇u=f
(with A random, non-necessarily symmetric) for the first time. When going from
p=2 to p>2, the main difficulty is to analyze the associated linearized operator,
whose coefficients are degenerate, unbounded, and depend on the random input A
via the solution of a nonlinear equation. One of our main achievements is the
control of this intricate nonlinear dependence, leading to annealed Meyers' estimates
for the linearized operator, which are key to the quantitative two-scale expansion
result.
acknowledgement: The authors warmly thank Mitia Duerinckx for discussions on annealed
estimates, and Mathias Schäffner for pointing out that the conditions of [14] apply
to ̄a in the setting of Theorem 2.2 and for discussions on regularity theory for
operators with non-standard growth conditions. The authors received financial support
from the European Research Council (ERC) under the European Union’s Horizon 2020
research and innovation programme (Grant Agreement n◦ 864066).
article_number: '2104.04263'
article_processing_charge: No
arxiv: 1
author:
- first_name: Nicolas
full_name: Clozeau, Nicolas
id: fea1b376-906f-11eb-847d-b2c0cf46455b
last_name: Clozeau
- first_name: Antoine
full_name: Gloria, Antoine
last_name: Gloria
citation:
ama: 'Clozeau N, Gloria A. Quantitative nonlinear homogenization: control of oscillations.
arXiv.'
apa: 'Clozeau, N., & Gloria, A. (n.d.). Quantitative nonlinear homogenization:
control of oscillations. arXiv.'
chicago: 'Clozeau, Nicolas, and Antoine Gloria. “Quantitative Nonlinear Homogenization:
Control of Oscillations.” ArXiv, n.d.'
ieee: 'N. Clozeau and A. Gloria, “Quantitative nonlinear homogenization: control
of oscillations,” arXiv. .'
ista: 'Clozeau N, Gloria A. Quantitative nonlinear homogenization: control of oscillations.
arXiv, 2104.04263.'
mla: 'Clozeau, Nicolas, and Antoine Gloria. “Quantitative Nonlinear Homogenization:
Control of Oscillations.” ArXiv, 2104.04263.'
short: N. Clozeau, A. Gloria, ArXiv (n.d.).
date_created: 2021-10-23T10:50:55Z
date_published: 2021-04-09T00:00:00Z
date_updated: 2021-10-28T15:44:05Z
day: '09'
department:
- _id: JuFi
external_id:
arxiv:
- '2104.04263'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2104.04263
month: '04'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: submitted
status: public
title: 'Quantitative nonlinear homogenization: control of oscillations'
type: preprint
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
year: '2021'
...
---
_id: '10549'
abstract:
- lang: eng
text: We derive optimal-order homogenization rates for random nonlinear elliptic
PDEs with monotone nonlinearity in the uniformly elliptic case. More precisely,
for a random monotone operator on \mathbb {R}^d with stationary law (that is spatially
homogeneous statistics) and fast decay of correlations on scales larger than the
microscale \varepsilon >0, we establish homogenization error estimates of the
order \varepsilon in case d\geqq 3, and of the order \varepsilon |\log \varepsilon
|^{1/2} in case d=2. Previous results in nonlinear stochastic homogenization have
been limited to a small algebraic rate of convergence \varepsilon ^\delta . We
also establish error estimates for the approximation of the homogenized operator
by the method of representative volumes of the order (L/\varepsilon )^{-d/2} for
a representative volume of size L. Our results also hold in the case of systems
for which a (small-scale) C^{1,\alpha } regularity theory is available.
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria). SN acknowledges partial support by the Deutsche Forschungsgemeinschaft
(DFG, German Research Foundation) – project number 405009441.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Stefan
full_name: Neukamm, Stefan
last_name: Neukamm
citation:
ama: Fischer JL, Neukamm S. Optimal homogenization rates in stochastic homogenization
of nonlinear uniformly elliptic equations and systems. Archive for Rational
Mechanics and Analysis. 2021;242(1):343-452. doi:10.1007/s00205-021-01686-9
apa: Fischer, J. L., & Neukamm, S. (2021). Optimal homogenization rates in stochastic
homogenization of nonlinear uniformly elliptic equations and systems. Archive
for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-021-01686-9
chicago: Fischer, Julian L, and Stefan Neukamm. “Optimal Homogenization Rates in
Stochastic Homogenization of Nonlinear Uniformly Elliptic Equations and Systems.”
Archive for Rational Mechanics and Analysis. Springer Nature, 2021. https://doi.org/10.1007/s00205-021-01686-9.
ieee: J. L. Fischer and S. Neukamm, “Optimal homogenization rates in stochastic
homogenization of nonlinear uniformly elliptic equations and systems,” Archive
for Rational Mechanics and Analysis, vol. 242, no. 1. Springer Nature, pp.
343–452, 2021.
ista: Fischer JL, Neukamm S. 2021. Optimal homogenization rates in stochastic homogenization
of nonlinear uniformly elliptic equations and systems. Archive for Rational Mechanics
and Analysis. 242(1), 343–452.
mla: Fischer, Julian L., and Stefan Neukamm. “Optimal Homogenization Rates in Stochastic
Homogenization of Nonlinear Uniformly Elliptic Equations and Systems.” Archive
for Rational Mechanics and Analysis, vol. 242, no. 1, Springer Nature, 2021,
pp. 343–452, doi:10.1007/s00205-021-01686-9.
short: J.L. Fischer, S. Neukamm, Archive for Rational Mechanics and Analysis 242
(2021) 343–452.
date_created: 2021-12-16T12:12:33Z
date_published: 2021-06-30T00:00:00Z
date_updated: 2023-08-17T06:23:21Z
day: '30'
ddc:
- '530'
department:
- _id: JuFi
doi: 10.1007/s00205-021-01686-9
external_id:
arxiv:
- '1908.02273'
isi:
- '000668431200001'
file:
- access_level: open_access
checksum: cc830b739aed83ca2e32c4e0ce266a4c
content_type: application/pdf
creator: cchlebak
date_created: 2021-12-16T14:58:08Z
date_updated: 2021-12-16T14:58:08Z
file_id: '10558'
file_name: 2021_ArchRatMechAnalysis_Fischer.pdf
file_size: 1640121
relation: main_file
success: 1
file_date_updated: 2021-12-16T14:58:08Z
has_accepted_license: '1'
intvolume: ' 242'
isi: 1
issue: '1'
keyword:
- Mechanical Engineering
- Mathematics (miscellaneous)
- Analysis
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 343-452
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
eissn:
- 1432-0673
issn:
- 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal homogenization rates in stochastic homogenization of nonlinear uniformly
elliptic equations and systems
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 242
year: '2021'
...
---
_id: '10575'
abstract:
- lang: eng
text: The choice of the boundary conditions in mechanical problems has to reflect
the interaction of the considered material with the surface. Still the assumption
of the no-slip condition is preferred in order to avoid boundary terms in the
analysis and slipping effects are usually overlooked. Besides the “static slip
models”, there are phenomena that are not accurately described by them, e.g. at
the moment when the slip changes rapidly, the wall shear stress and the slip can
exhibit a sudden overshoot and subsequent relaxation. When these effects become
significant, the so-called dynamic slip phenomenon occurs. We develop a mathematical
analysis of Navier–Stokes-like problems with a dynamic slip boundary condition,
which requires a proper generalization of the Gelfand triplet and the corresponding
function space setting.
acknowledgement: The research of A. Abbatiello is supported by Einstein Foundation,
Berlin. A. Abbatiello is also member of the Italian National Group for the Mathematical
Physics (GNFM) of INdAM. M. Bulíček acknowledges the support of the project No.
20-11027X financed by Czech Science Foundation (GACR). M. Bulíček is member of the
Jindřich Nečas Center for Mathematical Modelling. E. Maringová acknowledges support
from Charles University Research program UNCE/SCI/023, the grant SVV-2020-260583
by the Ministry of Education, Youth and Sports, Czech Republic and from the Austrian
Science Fund (FWF), grants P30000, W1245, and F65.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Anna
full_name: Abbatiello, Anna
last_name: Abbatiello
- first_name: Miroslav
full_name: Bulíček, Miroslav
last_name: Bulíček
- first_name: Erika
full_name: Maringová, Erika
id: dbabca31-66eb-11eb-963a-fb9c22c880b4
last_name: Maringová
citation:
ama: Abbatiello A, Bulíček M, Maringová E. On the dynamic slip boundary condition
for Navier-Stokes-like problems. Mathematical Models and Methods in Applied
Sciences. 2021;31(11):2165-2212. doi:10.1142/S0218202521500470
apa: Abbatiello, A., Bulíček, M., & Maringová, E. (2021). On the dynamic slip
boundary condition for Navier-Stokes-like problems. Mathematical Models and
Methods in Applied Sciences. World Scientific Publishing. https://doi.org/10.1142/S0218202521500470
chicago: Abbatiello, Anna, Miroslav Bulíček, and Erika Maringová. “On the Dynamic
Slip Boundary Condition for Navier-Stokes-like Problems.” Mathematical Models
and Methods in Applied Sciences. World Scientific Publishing, 2021. https://doi.org/10.1142/S0218202521500470.
ieee: A. Abbatiello, M. Bulíček, and E. Maringová, “On the dynamic slip boundary
condition for Navier-Stokes-like problems,” Mathematical Models and Methods
in Applied Sciences, vol. 31, no. 11. World Scientific Publishing, pp. 2165–2212,
2021.
ista: Abbatiello A, Bulíček M, Maringová E. 2021. On the dynamic slip boundary condition
for Navier-Stokes-like problems. Mathematical Models and Methods in Applied Sciences.
31(11), 2165–2212.
mla: Abbatiello, Anna, et al. “On the Dynamic Slip Boundary Condition for Navier-Stokes-like
Problems.” Mathematical Models and Methods in Applied Sciences, vol. 31,
no. 11, World Scientific Publishing, 2021, pp. 2165–212, doi:10.1142/S0218202521500470.
short: A. Abbatiello, M. Bulíček, E. Maringová, Mathematical Models and Methods
in Applied Sciences 31 (2021) 2165–2212.
date_created: 2021-12-26T23:01:27Z
date_published: 2021-10-13T00:00:00Z
date_updated: 2023-08-17T06:29:01Z
day: '13'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1142/S0218202521500470
external_id:
arxiv:
- '2009.09057'
isi:
- '000722309400001'
file:
- access_level: open_access
checksum: 8c0a9396335f0b70e1f5cbfe450a987a
content_type: application/pdf
creator: dernst
date_created: 2022-05-16T10:55:45Z
date_updated: 2022-05-16T10:55:45Z
file_id: '11385'
file_name: 2021_MathModelsMethods_Abbatiello.pdf
file_size: 795483
relation: main_file
success: 1
file_date_updated: 2022-05-16T10:55:45Z
has_accepted_license: '1'
intvolume: ' 31'
isi: 1
issue: '11'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 2165-2212
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 260788DE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
name: Dissipation and Dispersion in Nonlinear Partial Differential Equations
publication: Mathematical Models and Methods in Applied Sciences
publication_identifier:
eissn:
- 1793-6314
issn:
- 0218-2025
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the dynamic slip boundary condition for Navier-Stokes-like problems
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 31
year: '2021'
...
---
_id: '7866'
abstract:
- lang: eng
text: In this paper, we establish convergence to equilibrium for a drift–diffusion–recombination
system modelling the charge transport within certain semiconductor devices. More
precisely, we consider a two-level system for electrons and holes which is augmented
by an intermediate energy level for electrons in so-called trapped states. The
recombination dynamics use the mass action principle by taking into account this
additional trap level. The main part of the paper is concerned with the derivation
of an entropy–entropy production inequality, which entails exponential convergence
to the equilibrium via the so-called entropy method. The novelty of our approach
lies in the fact that the entropy method is applied uniformly in a fast-reaction
parameter which governs the lifetime of electrons on the trap level. Thus, the
resulting decay estimate for the densities of electrons and holes extends to the
corresponding quasi-steady-state approximation.
acknowledgement: Open access funding provided by Austrian Science Fund (FWF). The
second author has been supported by the International Research Training Group IGDK
1754 “Optimization and Numerical Analysis for Partial Differential Equations with
Nonsmooth Structures”, funded by the German Research Council (DFG) and the Austrian
Science Fund (FWF) under grant number [W 1244-N18].
article_processing_charge: No
article_type: original
author:
- first_name: Klemens
full_name: Fellner, Klemens
last_name: Fellner
- first_name: Michael
full_name: Kniely, Michael
id: 2CA2C08C-F248-11E8-B48F-1D18A9856A87
last_name: Kniely
orcid: 0000-0001-5645-4333
citation:
ama: Fellner K, Kniely M. Uniform convergence to equilibrium for a family of drift–diffusion
models with trap-assisted recombination and the limiting Shockley–Read–Hall model.
Journal of Elliptic and Parabolic Equations. 2020;6:529-598. doi:10.1007/s41808-020-00068-8
apa: Fellner, K., & Kniely, M. (2020). Uniform convergence to equilibrium for
a family of drift–diffusion models with trap-assisted recombination and the limiting
Shockley–Read–Hall model. Journal of Elliptic and Parabolic Equations.
Springer Nature. https://doi.org/10.1007/s41808-020-00068-8
chicago: Fellner, Klemens, and Michael Kniely. “Uniform Convergence to Equilibrium
for a Family of Drift–Diffusion Models with Trap-Assisted Recombination and the
Limiting Shockley–Read–Hall Model.” Journal of Elliptic and Parabolic Equations.
Springer Nature, 2020. https://doi.org/10.1007/s41808-020-00068-8.
ieee: K. Fellner and M. Kniely, “Uniform convergence to equilibrium for a family
of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall
model,” Journal of Elliptic and Parabolic Equations, vol. 6. Springer Nature,
pp. 529–598, 2020.
ista: Fellner K, Kniely M. 2020. Uniform convergence to equilibrium for a family
of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall
model. Journal of Elliptic and Parabolic Equations. 6, 529–598.
mla: Fellner, Klemens, and Michael Kniely. “Uniform Convergence to Equilibrium for
a Family of Drift–Diffusion Models with Trap-Assisted Recombination and the Limiting
Shockley–Read–Hall Model.” Journal of Elliptic and Parabolic Equations,
vol. 6, Springer Nature, 2020, pp. 529–98, doi:10.1007/s41808-020-00068-8.
short: K. Fellner, M. Kniely, Journal of Elliptic and Parabolic Equations 6 (2020)
529–598.
date_created: 2020-05-17T22:00:45Z
date_published: 2020-12-01T00:00:00Z
date_updated: 2021-01-12T08:15:47Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s41808-020-00068-8
file:
- access_level: open_access
checksum: 6bc6832caacddceee1471291e93dcf1d
content_type: application/pdf
creator: dernst
date_created: 2020-11-25T08:59:59Z
date_updated: 2020-11-25T08:59:59Z
file_id: '8802'
file_name: 2020_JourEllipticParabEquat_Fellner.pdf
file_size: 8408694
relation: main_file
success: 1
file_date_updated: 2020-11-25T08:59:59Z
has_accepted_license: '1'
intvolume: ' 6'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 529-598
project:
- _id: 3AC91DDA-15DF-11EA-824D-93A3E7B544D1
call_identifier: FWF
name: FWF Open Access Fund
publication: Journal of Elliptic and Parabolic Equations
publication_identifier:
eissn:
- '22969039'
issn:
- '22969020'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Uniform convergence to equilibrium for a family of drift–diffusion models with
trap-assisted recombination and the limiting Shockley–Read–Hall model
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 6
year: '2020'
...