---
_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. <i>Communications in Partial Differential Equations</i>.
    2022;47(7):1394-1434. doi:<a href="https://doi.org/10.1080/03605302.2022.2056702">10.1080/03605302.2022.2056702</a>
  apa: De Nitti, N., &#38; Fischer, J. L. (2022). Sharp criteria for the waiting time
    phenomenon in solutions to the thin-film equation. <i>Communications in Partial
    Differential Equations</i>. Taylor &#38; Francis. <a href="https://doi.org/10.1080/03605302.2022.2056702">https://doi.org/10.1080/03605302.2022.2056702</a>
  chicago: De Nitti, Nicola, and Julian L Fischer. “Sharp Criteria for the Waiting
    Time Phenomenon in Solutions to the Thin-Film Equation.” <i>Communications in
    Partial Differential Equations</i>. Taylor &#38; Francis, 2022. <a href="https://doi.org/10.1080/03605302.2022.2056702">https://doi.org/10.1080/03605302.2022.2056702</a>.
  ieee: N. De Nitti and J. L. Fischer, “Sharp criteria for the waiting time phenomenon
    in solutions to the thin-film equation,” <i>Communications in Partial Differential
    Equations</i>, vol. 47, no. 7. Taylor &#38; 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.” <i>Communications in Partial
    Differential Equations</i>, vol. 47, no. 7, Taylor &#38; Francis, 2022, pp. 1394–434,
    doi:<a href="https://doi.org/10.1080/03605302.2022.2056702">10.1080/03605302.2022.2056702</a>.
  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'
...