[{"scopus_import":"1","license":"https://creativecommons.org/licenses/by/3.0/","_id":"8697","issue":"11","author":[{"last_name":"Fischer","first_name":"Julian L","full_name":"Fischer, Julian L","orcid":"0000-0002-0479-558X","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87"},{"id":"2CA2C08C-F248-11E8-B48F-1D18A9856A87","full_name":"Kniely, Michael","orcid":"0000-0001-5645-4333","last_name":"Kniely","first_name":"Michael"}],"article_processing_charge":"Yes (via OA deal)","date_created":"2020-10-25T23:01:16Z","department":[{"_id":"JuFi"}],"publication_status":"published","intvolume":"        33","title":"Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model","quality_controlled":"1","page":"5733-5772","file_date_updated":"2020-10-27T12:09:57Z","publisher":"IOP Publishing","article_type":"original","year":"2020","citation":{"ama":"Fischer JL, Kniely M. Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model. <i>Nonlinearity</i>. 2020;33(11):5733-5772. doi:<a href=\"https://doi.org/10.1088/1361-6544/ab9728\">10.1088/1361-6544/ab9728</a>","apa":"Fischer, J. L., &#38; Kniely, M. (2020). Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model. <i>Nonlinearity</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/1361-6544/ab9728\">https://doi.org/10.1088/1361-6544/ab9728</a>","ieee":"J. L. Fischer and M. Kniely, “Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model,” <i>Nonlinearity</i>, vol. 33, no. 11. IOP Publishing, pp. 5733–5772, 2020.","chicago":"Fischer, Julian L, and Michael Kniely. “Variance Reduction for Effective Energies of Random Lattices in the Thomas-Fermi-von Weizsäcker Model.” <i>Nonlinearity</i>. IOP Publishing, 2020. <a href=\"https://doi.org/10.1088/1361-6544/ab9728\">https://doi.org/10.1088/1361-6544/ab9728</a>.","mla":"Fischer, Julian L., and Michael Kniely. “Variance Reduction for Effective Energies of Random Lattices in the Thomas-Fermi-von Weizsäcker Model.” <i>Nonlinearity</i>, vol. 33, no. 11, IOP Publishing, 2020, pp. 5733–72, doi:<a href=\"https://doi.org/10.1088/1361-6544/ab9728\">10.1088/1361-6544/ab9728</a>.","short":"J.L. Fischer, M. Kniely, Nonlinearity 33 (2020) 5733–5772.","ista":"Fischer JL, Kniely M. 2020. Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model. Nonlinearity. 33(11), 5733–5772."},"date_updated":"2023-08-22T10:38:38Z","external_id":{"arxiv":["1906.12245"],"isi":["000576492700001"]},"isi":1,"day":"01","doi":"10.1088/1361-6544/ab9728","arxiv":1,"abstract":[{"lang":"eng","text":"In the computation of the material properties of random alloys, the method of 'special quasirandom structures' attempts to approximate the properties of the alloy on a finite volume with higher accuracy by replicating certain statistics of the random atomic lattice in the finite volume as accurately as possible. In the present work, we provide a rigorous justification for a variant of this method in the framework of the Thomas–Fermi–von Weizsäcker (TFW) model. Our approach is based on a recent analysis of a related variance reduction method in stochastic homogenization of linear elliptic PDEs and the locality properties of the TFW model. Concerning the latter, we extend an exponential locality result by Nazar and Ortner to include point charges, a result that may be of independent interest."}],"volume":33,"ddc":["510"],"has_accepted_license":"1","publication":"Nonlinearity","oa_version":"Published Version","month":"11","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)","image":"/images/cc_by.png","short":"CC BY (3.0)","legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode"},"type":"journal_article","date_published":"2020-11-01T00:00:00Z","publication_identifier":{"eissn":["13616544"],"issn":["09517715"]},"oa":1,"file":[{"date_created":"2020-10-27T12:09:57Z","file_size":1223899,"checksum":"ed90bc6eb5f32ee6157fef7f3aabc057","date_updated":"2020-10-27T12:09:57Z","file_name":"2020_Nonlinearity_Fischer.pdf","content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"8710","creator":"cziletti"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"has_accepted_license":"1","publication":"Archive for Rational Mechanics and Analysis","project":[{"call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"oa_version":"Published Version","month":"05","language":[{"iso":"eng"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","date_published":"2020-05-01T00:00:00Z","publication_identifier":{"eissn":["14320673"],"issn":["00039527"]},"oa":1,"file":[{"date_updated":"2020-11-20T09:14:22Z","content_type":"application/pdf","file_name":"2020_ArchRatMechAn_Fischer.pdf","date_created":"2020-11-20T09:14:22Z","file_size":1897571,"checksum":"f107e21b58f5930876f47144be37cf6c","file_id":"8779","creator":"dernst","success":1,"relation":"main_file","access_level":"open_access"}],"status":"public","related_material":{"record":[{"status":"public","id":"10007","relation":"dissertation_contains"}]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","scopus_import":"1","_id":"7489","author":[{"id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","full_name":"Fischer, Julian L","orcid":"0000-0002-0479-558X","last_name":"Fischer","first_name":"Julian L"},{"full_name":"Hensel, Sebastian","orcid":"0000-0001-7252-8072","last_name":"Hensel","first_name":"Sebastian","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"Yes (via OA deal)","department":[{"_id":"JuFi"}],"date_created":"2020-02-16T23:00:50Z","publication_status":"published","intvolume":"       236","title":"Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface tension","ec_funded":1,"quality_controlled":"1","page":"967-1087","file_date_updated":"2020-11-20T09:14:22Z","publisher":"Springer Nature","article_type":"original","citation":{"ista":"Fischer JL, Hensel S. 2020. Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface tension. Archive for Rational Mechanics and Analysis. 236, 967–1087.","mla":"Fischer, Julian L., and Sebastian Hensel. “Weak–Strong Uniqueness for the Navier–Stokes Equation for Two Fluids with Surface Tension.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 236, Springer Nature, 2020, pp. 967–1087, doi:<a href=\"https://doi.org/10.1007/s00205-019-01486-2\">10.1007/s00205-019-01486-2</a>.","short":"J.L. Fischer, S. Hensel, Archive for Rational Mechanics and Analysis 236 (2020) 967–1087.","chicago":"Fischer, Julian L, and Sebastian Hensel. “Weak–Strong Uniqueness for the Navier–Stokes Equation for Two Fluids with Surface Tension.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00205-019-01486-2\">https://doi.org/10.1007/s00205-019-01486-2</a>.","ieee":"J. L. Fischer and S. Hensel, “Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface tension,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 236. Springer Nature, pp. 967–1087, 2020.","apa":"Fischer, J. L., &#38; Hensel, S. (2020). Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface tension. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-019-01486-2\">https://doi.org/10.1007/s00205-019-01486-2</a>","ama":"Fischer JL, Hensel S. Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface tension. <i>Archive for Rational Mechanics and Analysis</i>. 2020;236:967-1087. doi:<a href=\"https://doi.org/10.1007/s00205-019-01486-2\">10.1007/s00205-019-01486-2</a>"},"year":"2020","date_updated":"2023-09-07T13:30:45Z","external_id":{"isi":["000511060200001"]},"isi":1,"day":"01","doi":"10.1007/s00205-019-01486-2","abstract":[{"text":"In the present work, we consider the evolution of two fluids separated by a sharp interface in the presence of surface tension—like, for example, the evolution of oil bubbles in water. Our main result is a weak–strong uniqueness principle for the corresponding free boundary problem for the incompressible Navier–Stokes equation: as long as a strong solution exists, any varifold solution must coincide with it. In particular, in the absence of physical singularities, the concept of varifold solutions—whose global in time existence has been shown by Abels (Interfaces Free Bound 9(1):31–65, 2007) for general initial data—does not introduce a mechanism for non-uniqueness. The key ingredient of our approach is the construction of a relative entropy functional capable of controlling the interface error. If the viscosities of the two fluids do not coincide, even for classical (strong) solutions the gradient of the velocity field becomes discontinuous at the interface, introducing the need for a careful additional adaption of the relative entropy.","lang":"eng"}],"volume":236,"ddc":["530","532"]},{"_id":"7637","scopus_import":"1","author":[{"id":"2CEB641C-A400-11E9-A717-D712E6697425","orcid":"0000-0002-6269-5149","full_name":"Cornalba, Federico","first_name":"Federico","last_name":"Cornalba"},{"full_name":"Shardlow, Tony","first_name":"Tony","last_name":"Shardlow"},{"full_name":"Zimmer, Johannes","first_name":"Johannes","last_name":"Zimmer"}],"issue":"2","publication_status":"published","date_created":"2020-04-05T22:00:49Z","department":[{"_id":"JuFi"}],"article_processing_charge":"No","title":"From weakly interacting particles to a regularised Dean-Kawasaki model","intvolume":"        33","page":"864-891","quality_controlled":"1","publisher":"IOP Publishing","article_type":"original","date_updated":"2023-08-18T10:26:07Z","year":"2020","citation":{"ama":"Cornalba F, Shardlow T, Zimmer J. From weakly interacting particles to a regularised Dean-Kawasaki model. <i>Nonlinearity</i>. 2020;33(2):864-891. doi:<a href=\"https://doi.org/10.1088/1361-6544/ab5174\">10.1088/1361-6544/ab5174</a>","apa":"Cornalba, F., Shardlow, T., &#38; Zimmer, J. (2020). From weakly interacting particles to a regularised Dean-Kawasaki model. <i>Nonlinearity</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/1361-6544/ab5174\">https://doi.org/10.1088/1361-6544/ab5174</a>","ieee":"F. Cornalba, T. Shardlow, and J. Zimmer, “From weakly interacting particles to a regularised Dean-Kawasaki model,” <i>Nonlinearity</i>, vol. 33, no. 2. IOP Publishing, pp. 864–891, 2020.","chicago":"Cornalba, Federico, Tony Shardlow, and Johannes Zimmer. “From Weakly Interacting Particles to a Regularised Dean-Kawasaki Model.” <i>Nonlinearity</i>. IOP Publishing, 2020. <a href=\"https://doi.org/10.1088/1361-6544/ab5174\">https://doi.org/10.1088/1361-6544/ab5174</a>.","short":"F. Cornalba, T. Shardlow, J. Zimmer, Nonlinearity 33 (2020) 864–891.","mla":"Cornalba, Federico, et al. “From Weakly Interacting Particles to a Regularised Dean-Kawasaki Model.” <i>Nonlinearity</i>, vol. 33, no. 2, IOP Publishing, 2020, pp. 864–91, doi:<a href=\"https://doi.org/10.1088/1361-6544/ab5174\">10.1088/1361-6544/ab5174</a>.","ista":"Cornalba F, Shardlow T, Zimmer J. 2020. From weakly interacting particles to a regularised Dean-Kawasaki model. Nonlinearity. 33(2), 864–891."},"isi":1,"external_id":{"isi":["000508175400001"],"arxiv":["1811.06448"]},"arxiv":1,"doi":"10.1088/1361-6544/ab5174","day":"10","abstract":[{"text":"The evolution of finitely many particles obeying Langevin dynamics is described by Dean–Kawasaki equations, a class of stochastic equations featuring a non-Lipschitz multiplicative noise in divergence form. We derive a regularised Dean–Kawasaki model based on second order Langevin dynamics by analysing a system of particles interacting via a pairwise potential. Key tools of our analysis are the propagation of chaos and Simon's compactness criterion. The model we obtain is a small-noise stochastic perturbation of the undamped McKean–Vlasov equation. We also provide a high-probability result for existence and uniqueness for our model.","lang":"eng"}],"volume":33,"publication":"Nonlinearity","oa_version":"Preprint","month":"01","language":[{"iso":"eng"}],"date_published":"2020-01-10T00:00:00Z","type":"journal_article","publication_identifier":{"issn":["09517715"],"eissn":["13616544"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1811.06448"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public"},{"ddc":["510"],"acknowledgement":"This work was supported by the European Union's Horizon 2020 Research and Innovation\r\nProgramme under Marie Sklodowska-Curie grant agreement 665385 and by the Deutsche\r\nForschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy, EXC-2047/1--390685813.","volume":52,"isi":1,"external_id":{"isi":["000600695200027"]},"date_updated":"2023-08-24T11:15:16Z","year":"2020","citation":{"chicago":"Fischer, Julian L, Tim Laux, and Theresa M. Simon. “Convergence Rates of the Allen-Cahn Equation to Mean Curvature Flow: A Short Proof Based on Relative Entropies.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics, 2020. <a href=\"https://doi.org/10.1137/20M1322182\">https://doi.org/10.1137/20M1322182</a>.","ieee":"J. L. Fischer, T. Laux, and T. M. Simon, “Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 52, no. 6. Society for Industrial and Applied Mathematics, pp. 6222–6233, 2020.","ama":"Fischer JL, Laux T, Simon TM. Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies. <i>SIAM Journal on Mathematical Analysis</i>. 2020;52(6):6222-6233. doi:<a href=\"https://doi.org/10.1137/20M1322182\">10.1137/20M1322182</a>","apa":"Fischer, J. L., Laux, T., &#38; Simon, T. M. (2020). Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/20M1322182\">https://doi.org/10.1137/20M1322182</a>","ista":"Fischer JL, Laux T, Simon TM. 2020. Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies. SIAM Journal on Mathematical Analysis. 52(6), 6222–6233.","short":"J.L. Fischer, T. Laux, T.M. Simon, SIAM Journal on Mathematical Analysis 52 (2020) 6222–6233.","mla":"Fischer, Julian L., et al. “Convergence Rates of the Allen-Cahn Equation to Mean Curvature Flow: A Short Proof Based on Relative Entropies.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 52, no. 6, Society for Industrial and Applied Mathematics, 2020, pp. 6222–33, doi:<a href=\"https://doi.org/10.1137/20M1322182\">10.1137/20M1322182</a>."},"abstract":[{"text":"We give a short and self-contained proof for rates of convergence of the Allen--Cahn equation towards mean curvature flow, assuming that a classical (smooth) solution to the latter exists and starting from well-prepared initial data. Our approach is based on a relative entropy technique. In particular, it does not require a stability analysis for the linearized Allen--Cahn operator. As our analysis also does not rely on the comparison principle, we expect it to be applicable to more complex equations and systems.","lang":"eng"}],"doi":"10.1137/20M1322182","day":"15","file_date_updated":"2021-01-25T07:48:39Z","page":"6222-6233","quality_controlled":"1","ec_funded":1,"article_type":"original","publisher":"Society for Industrial and Applied Mathematics","author":[{"id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer","first_name":"Julian L","full_name":"Fischer, Julian L","orcid":"0000-0002-0479-558X"},{"first_name":"Tim","last_name":"Laux","full_name":"Laux, Tim"},{"full_name":"Simon, Theresa M.","last_name":"Simon","first_name":"Theresa M."}],"issue":"6","_id":"9039","scopus_import":"1","title":"Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies","intvolume":"        52","publication_status":"published","article_processing_charge":"No","date_created":"2021-01-24T23:01:09Z","department":[{"_id":"JuFi"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"access_level":"open_access","success":1,"relation":"main_file","creator":"dernst","file_id":"9041","checksum":"21aa1cf4c30a86a00cae15a984819b5d","file_size":310655,"date_created":"2021-01-25T07:48:39Z","content_type":"application/pdf","file_name":"2020_SIAM_Fischer.pdf","date_updated":"2021-01-25T07:48:39Z"}],"date_published":"2020-12-15T00:00:00Z","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"publication_identifier":{"eissn":["10957154"],"issn":["00361410"]},"language":[{"iso":"eng"}],"publication":"SIAM Journal on Mathematical Analysis","has_accepted_license":"1","month":"12","oa_version":"Published Version","project":[{"grant_number":"665385","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}]},{"volume":252,"abstract":[{"text":"In order to provide a local description of a regular function in a small neighbourhood of a point x, it is sufficient by Taylor’s theorem to know the value of the function as well as all of its derivatives up to the required order at the point x itself. In other words, one could say that a regular function is locally modelled by the set of polynomials. The theory of regularity structures due to Hairer generalizes this observation and provides an abstract setup, which in the application to singular SPDE extends the set of polynomials by functionals constructed from, e.g., white noise. In this context, the notion of Taylor polynomials is lifted to the notion of so-called modelled distributions. The celebrated reconstruction theorem, which in turn was inspired by Gubinelli’s \\textit {sewing lemma}, is of paramount importance for the theory. It enables one to reconstruct a modelled distribution as a true distribution on Rd which is locally approximated by this extended set of models or “monomials”. In the original work of Hairer, the error is measured by means of Hölder norms. This was then generalized to the whole scale of Besov spaces by Hairer and Labbé. It is the aim of this work to adapt the analytic part of the theory of regularity structures to the scale of Triebel–Lizorkin spaces.","lang":"eng"}],"day":"01","doi":"10.4064/sm180411-11-2","arxiv":1,"external_id":{"isi":["000558100500002"],"arxiv":["1709.05202"]},"isi":1,"citation":{"apa":"Hensel, S., &#38; Rosati, T. (2020). Modelled distributions of Triebel–Lizorkin type. <i>Studia Mathematica</i>. Instytut Matematyczny. <a href=\"https://doi.org/10.4064/sm180411-11-2\">https://doi.org/10.4064/sm180411-11-2</a>","ama":"Hensel S, Rosati T. Modelled distributions of Triebel–Lizorkin type. <i>Studia Mathematica</i>. 2020;252(3):251-297. doi:<a href=\"https://doi.org/10.4064/sm180411-11-2\">10.4064/sm180411-11-2</a>","ieee":"S. Hensel and T. Rosati, “Modelled distributions of Triebel–Lizorkin type,” <i>Studia Mathematica</i>, vol. 252, no. 3. Instytut Matematyczny, pp. 251–297, 2020.","chicago":"Hensel, Sebastian, and Tommaso Rosati. “Modelled Distributions of Triebel–Lizorkin Type.” <i>Studia Mathematica</i>. Instytut Matematyczny, 2020. <a href=\"https://doi.org/10.4064/sm180411-11-2\">https://doi.org/10.4064/sm180411-11-2</a>.","mla":"Hensel, Sebastian, and Tommaso Rosati. “Modelled Distributions of Triebel–Lizorkin Type.” <i>Studia Mathematica</i>, vol. 252, no. 3, Instytut Matematyczny, 2020, pp. 251–97, doi:<a href=\"https://doi.org/10.4064/sm180411-11-2\">10.4064/sm180411-11-2</a>.","short":"S. Hensel, T. Rosati, Studia Mathematica 252 (2020) 251–297.","ista":"Hensel S, Rosati T. 2020. Modelled distributions of Triebel–Lizorkin type. Studia Mathematica. 252(3), 251–297."},"year":"2020","date_updated":"2023-10-17T09:15:53Z","article_type":"original","publisher":"Instytut Matematyczny","quality_controlled":"1","page":"251-297","intvolume":"       252","title":"Modelled distributions of Triebel–Lizorkin type","article_processing_charge":"No","date_created":"2021-02-25T08:55:03Z","department":[{"_id":"JuFi"},{"_id":"GradSch"}],"publication_status":"published","issue":"3","author":[{"id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","first_name":"Sebastian","last_name":"Hensel","orcid":"0000-0001-7252-8072","full_name":"Hensel, Sebastian"},{"full_name":"Rosati, Tommaso","last_name":"Rosati","first_name":"Tommaso"}],"scopus_import":"1","_id":"9196","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["0039-3223"],"eissn":["1730-6337"]},"type":"journal_article","date_published":"2020-03-01T00:00:00Z","keyword":["General Mathematics"],"language":[{"iso":"eng"}],"month":"03","oa_version":"Preprint","publication":"Studia Mathematica"},{"title":"The local structure of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions","month":"03","article_number":"2003.05478","oa_version":"Preprint","publication_status":"submitted","article_processing_charge":"No","department":[{"_id":"JuFi"}],"project":[{"call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program"}],"date_created":"2021-09-13T12:17:11Z","author":[{"id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","first_name":"Julian L","last_name":"Fischer","orcid":"0000-0002-0479-558X","full_name":"Fischer, Julian L"},{"id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","full_name":"Hensel, Sebastian","orcid":"0000-0001-7252-8072","last_name":"Hensel","first_name":"Sebastian"},{"last_name":"Laux","first_name":"Tim","full_name":"Laux, Tim"},{"last_name":"Simon","first_name":"Thilo","full_name":"Simon, Thilo"}],"publication":"arXiv","_id":"10012","language":[{"iso":"eng"}],"ec_funded":1,"abstract":[{"lang":"eng","text":"We prove that in the absence of topological changes, the notion of BV solutions to planar multiphase mean curvature flow does not allow for a mechanism for (unphysical) non-uniqueness. Our approach is based on the local structure of the energy landscape near a classical evolution by mean curvature. Mean curvature flow being the gradient flow of the surface energy functional, we develop a gradient-flow analogue of the notion of calibrations. Just like the existence of a calibration guarantees that one has reached a global minimum in the energy landscape, the existence of a \"gradient flow calibration\" ensures that the route of steepest descent in the energy landscape is unique and stable."}],"oa":1,"arxiv":1,"day":"11","date_published":"2020-03-11T00:00:00Z","type":"preprint","external_id":{"arxiv":["2003.05478"]},"date_updated":"2023-09-07T13:30:45Z","citation":{"ista":"Fischer JL, Hensel S, Laux T, Simon T. The local structure of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions. arXiv, 2003.05478.","short":"J.L. Fischer, S. Hensel, T. Laux, T. Simon, ArXiv (n.d.).","mla":"Fischer, Julian L., et al. “The Local Structure of the Energy Landscape in Multiphase Mean Curvature Flow: Weak-Strong Uniqueness and Stability of Evolutions.” <i>ArXiv</i>, 2003.05478.","chicago":"Fischer, Julian L, Sebastian Hensel, Tim Laux, and Thilo Simon. “The Local Structure of the Energy Landscape in Multiphase Mean Curvature Flow: Weak-Strong Uniqueness and Stability of Evolutions.” <i>ArXiv</i>, n.d.","ieee":"J. L. Fischer, S. Hensel, T. Laux, and T. Simon, “The local structure of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions,” <i>arXiv</i>. .","ama":"Fischer JL, Hensel S, Laux T, Simon T. The local structure of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions. <i>arXiv</i>.","apa":"Fischer, J. L., Hensel, S., Laux, T., &#38; Simon, T. (n.d.). The local structure of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions. <i>arXiv</i>."},"year":"2020","related_material":{"record":[{"status":"public","id":"10007","relation":"dissertation_contains"}]},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","status":"public","acknowledgement":"Parts of the paper were written during the visit of the authors to the Hausdorff Research Institute for Mathematics (HIM), University of Bonn, in the framework of the trimester program “Evolution of Interfaces”. The support and the hospitality of HIM are gratefully acknowledged. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 665385.","main_file_link":[{"url":"https://arxiv.org/abs/2003.05478","open_access":"1"}]},{"author":[{"full_name":"Fischer, Julian L","orcid":"0000-0002-0479-558X","last_name":"Fischer","first_name":"Julian L","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87"}],"issue":"2","_id":"6617","scopus_import":"1","title":"The choice of representative volumes in the approximation of effective properties of random materials","intvolume":"       234","publication_status":"published","article_processing_charge":"Yes (via OA deal)","department":[{"_id":"JuFi"}],"date_created":"2019-07-07T21:59:23Z","file_date_updated":"2020-07-14T12:47:34Z","page":"635–726","quality_controlled":"1","article_type":"original","publisher":"Springer","isi":1,"external_id":{"isi":["000482386000006"],"arxiv":["1807.00834"]},"date_updated":"2023-08-28T12:31:21Z","citation":{"apa":"Fischer, J. L. (2019). The choice of representative volumes in the approximation of effective properties of random materials. <i>Archive for Rational Mechanics and Analysis</i>. Springer. <a href=\"https://doi.org/10.1007/s00205-019-01400-w\">https://doi.org/10.1007/s00205-019-01400-w</a>","ama":"Fischer JL. The choice of representative volumes in the approximation of effective properties of random materials. <i>Archive for Rational Mechanics and Analysis</i>. 2019;234(2):635–726. doi:<a href=\"https://doi.org/10.1007/s00205-019-01400-w\">10.1007/s00205-019-01400-w</a>","ieee":"J. L. Fischer, “The choice of representative volumes in the approximation of effective properties of random materials,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 234, no. 2. Springer, pp. 635–726, 2019.","chicago":"Fischer, Julian L. “The Choice of Representative Volumes in the Approximation of Effective Properties of Random Materials.” <i>Archive for Rational Mechanics and Analysis</i>. Springer, 2019. <a href=\"https://doi.org/10.1007/s00205-019-01400-w\">https://doi.org/10.1007/s00205-019-01400-w</a>.","mla":"Fischer, Julian L. “The Choice of Representative Volumes in the Approximation of Effective Properties of Random Materials.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 234, no. 2, Springer, 2019, pp. 635–726, doi:<a href=\"https://doi.org/10.1007/s00205-019-01400-w\">10.1007/s00205-019-01400-w</a>.","short":"J.L. Fischer, Archive for Rational Mechanics and Analysis 234 (2019) 635–726.","ista":"Fischer JL. 2019. The choice of representative volumes in the approximation of effective properties of random materials. Archive for Rational Mechanics and Analysis. 234(2), 635–726."},"year":"2019","abstract":[{"text":"The effective large-scale properties of materials with random heterogeneities on a small scale are typically determined by the method of representative volumes: a sample of the random material is chosen—the representative volume—and its effective properties are computed by the cell formula. Intuitively, for a fixed sample size it should be possible to increase the accuracy of the method by choosing a material sample which captures the statistical properties of the material particularly well; for example, for a composite material consisting of two constituents, one would select a representative volume in which the volume fraction of the constituents matches closely with their volume fraction in the overall material. Inspired by similar attempts in materials science, Le Bris, Legoll and Minvielle have designed a selection approach for representative volumes which performs remarkably well in numerical examples of linear materials with moderate contrast. In the present work, we provide a rigorous analysis of this selection approach for representative volumes in the context of stochastic homogenization of linear elliptic equations. In particular, we prove that the method essentially never performs worse than a random selection of the material sample and may perform much better if the selection criterion for the material samples is chosen suitably.","lang":"eng"}],"doi":"10.1007/s00205-019-01400-w","arxiv":1,"day":"01","ddc":["500"],"volume":234,"publication":"Archive for Rational Mechanics and Analysis","has_accepted_license":"1","month":"11","oa_version":"Published Version","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"language":[{"iso":"eng"}],"date_published":"2019-11-01T00:00:00Z","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"creator":"kschuh","file_id":"6626","relation":"main_file","access_level":"open_access","file_name":"Springer_2019_Fischer.pdf","content_type":"application/pdf","date_updated":"2020-07-14T12:47:34Z","file_size":1377659,"checksum":"4cff75fa6addb0770991ad9c474ab404","date_created":"2019-07-08T15:56:47Z"}]},{"language":[{"iso":"eng"}],"oa_version":"Preprint","month":"07","publication":"Multiscale Modeling and Simulation","main_file_link":[{"url":"https://arxiv.org/abs/1808.04200","open_access":"1"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","publication_identifier":{"eissn":["15403467"],"issn":["15403459"]},"oa":1,"type":"journal_article","date_published":"2019-07-16T00:00:00Z","publisher":"SIAM","quality_controlled":"1","page":"926-947","date_created":"2019-08-04T21:59:21Z","department":[{"_id":"JuFi"}],"article_processing_charge":"No","publication_status":"published","intvolume":"        17","title":"New optimal control problems in density functional theory motivated by photovoltaics","scopus_import":"1","_id":"6762","issue":"3","author":[{"first_name":"Gero","last_name":"Friesecke","full_name":"Friesecke, Gero"},{"id":"2CA2C08C-F248-11E8-B48F-1D18A9856A87","first_name":"Michael","last_name":"Kniely","orcid":"0000-0001-5645-4333","full_name":"Kniely, Michael"}],"volume":17,"day":"16","doi":"10.1137/18M1207272","arxiv":1,"abstract":[{"lang":"eng","text":"We present and study novel optimal control problems motivated by the search for photovoltaic materials with high power-conversion efficiency. The material must perform the first step: convert light (photons) into electronic excitations. We formulate various desirable properties of the excitations as mathematical control goals at the Kohn-Sham-DFT level\r\nof theory, with the control being given by the nuclear charge distribution. We prove that nuclear distributions exist which give rise to optimal HOMO-LUMO excitations, and present illustrative numerical simulations for 1D finite nanocrystals. We observe pronounced goal-dependent features such as large electron-hole separation, and a hierarchy of length scales: internal HOMO and LUMO wavelengths < atomic spacings < (irregular) fluctuations of the doping profiles < system size."}],"year":"2019","citation":{"short":"G. Friesecke, M. Kniely, Multiscale Modeling and Simulation 17 (2019) 926–947.","mla":"Friesecke, Gero, and Michael Kniely. “New Optimal Control Problems in Density Functional Theory Motivated by Photovoltaics.” <i>Multiscale Modeling and Simulation</i>, vol. 17, no. 3, SIAM, 2019, pp. 926–47, doi:<a href=\"https://doi.org/10.1137/18M1207272\">10.1137/18M1207272</a>.","ista":"Friesecke G, Kniely M. 2019. New optimal control problems in density functional theory motivated by photovoltaics. Multiscale Modeling and Simulation. 17(3), 926–947.","ama":"Friesecke G, Kniely M. New optimal control problems in density functional theory motivated by photovoltaics. <i>Multiscale Modeling and Simulation</i>. 2019;17(3):926-947. doi:<a href=\"https://doi.org/10.1137/18M1207272\">10.1137/18M1207272</a>","apa":"Friesecke, G., &#38; Kniely, M. (2019). New optimal control problems in density functional theory motivated by photovoltaics. <i>Multiscale Modeling and Simulation</i>. SIAM. <a href=\"https://doi.org/10.1137/18M1207272\">https://doi.org/10.1137/18M1207272</a>","ieee":"G. Friesecke and M. Kniely, “New optimal control problems in density functional theory motivated by photovoltaics,” <i>Multiscale Modeling and Simulation</i>, vol. 17, no. 3. SIAM, pp. 926–947, 2019.","chicago":"Friesecke, Gero, and Michael Kniely. “New Optimal Control Problems in Density Functional Theory Motivated by Photovoltaics.” <i>Multiscale Modeling and Simulation</i>. SIAM, 2019. <a href=\"https://doi.org/10.1137/18M1207272\">https://doi.org/10.1137/18M1207272</a>."},"date_updated":"2023-09-05T15:05:45Z","external_id":{"arxiv":["1808.04200"],"isi":["000487931800002"]},"isi":1},{"page":"257 - 311","quality_controlled":"1","publisher":"Elsevier","author":[{"id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer","first_name":"Julian L","full_name":"Fischer, Julian L","orcid":"0000-0002-0479-558X"},{"last_name":"Kneuss","first_name":"Olivier","full_name":"Kneuss, Olivier"}],"issue":"1","_id":"151","scopus_import":"1","title":"Bi-Sobolev solutions to the prescribed Jacobian inequality in the plane with L p data and applications to nonlinear elasticity","intvolume":"       266","publication_status":"published","article_processing_charge":"No","date_created":"2018-12-11T11:44:54Z","department":[{"_id":"JuFi"}],"volume":266,"isi":1,"external_id":{"isi":["000449108500010"],"arxiv":["1408.1587"]},"date_updated":"2023-09-08T13:25:35Z","year":"2019","citation":{"ista":"Fischer JL, Kneuss O. 2019. Bi-Sobolev solutions to the prescribed Jacobian inequality in the plane with L p data and applications to nonlinear elasticity. Journal of Differential Equations. 266(1), 257–311.","mla":"Fischer, Julian L., and Olivier Kneuss. “Bi-Sobolev Solutions to the Prescribed Jacobian Inequality in the Plane with L p Data and Applications to Nonlinear Elasticity.” <i>Journal of Differential Equations</i>, vol. 266, no. 1, Elsevier, 2019, pp. 257–311, doi:<a href=\"https://doi.org/10.1016/j.jde.2018.07.045\">10.1016/j.jde.2018.07.045</a>.","short":"J.L. Fischer, O. Kneuss, Journal of Differential Equations 266 (2019) 257–311.","chicago":"Fischer, Julian L, and Olivier Kneuss. “Bi-Sobolev Solutions to the Prescribed Jacobian Inequality in the Plane with L p Data and Applications to Nonlinear Elasticity.” <i>Journal of Differential Equations</i>. Elsevier, 2019. <a href=\"https://doi.org/10.1016/j.jde.2018.07.045\">https://doi.org/10.1016/j.jde.2018.07.045</a>.","ieee":"J. L. Fischer and O. Kneuss, “Bi-Sobolev solutions to the prescribed Jacobian inequality in the plane with L p data and applications to nonlinear elasticity,” <i>Journal of Differential Equations</i>, vol. 266, no. 1. Elsevier, pp. 257–311, 2019.","ama":"Fischer JL, Kneuss O. Bi-Sobolev solutions to the prescribed Jacobian inequality in the plane with L p data and applications to nonlinear elasticity. <i>Journal of Differential Equations</i>. 2019;266(1):257-311. doi:<a href=\"https://doi.org/10.1016/j.jde.2018.07.045\">10.1016/j.jde.2018.07.045</a>","apa":"Fischer, J. L., &#38; Kneuss, O. (2019). Bi-Sobolev solutions to the prescribed Jacobian inequality in the plane with L p data and applications to nonlinear elasticity. <i>Journal of Differential Equations</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jde.2018.07.045\">https://doi.org/10.1016/j.jde.2018.07.045</a>"},"abstract":[{"text":"We construct planar bi-Sobolev mappings whose local volume distortion is bounded from below by a given function f∈Lp with p&gt;1. More precisely, for any 1&lt;q&lt;(p+1)/2 we construct W1,q-bi-Sobolev maps with identity boundary conditions; for f∈L∞, we provide bi-Lipschitz maps. The basic building block of our construction are bi-Lipschitz maps which stretch a given compact subset of the unit square by a given factor while preserving the boundary. The construction of these stretching maps relies on a slight strengthening of the celebrated covering result of Alberti, Csörnyei, and Preiss for measurable planar sets in the case of compact sets. We apply our result to a model functional in nonlinear elasticity, the integrand of which features fast blowup as the Jacobian determinant of the deformation becomes small. For such functionals, the derivation of the equilibrium equations for minimizers requires an additional regularization of test functions, which our maps provide.","lang":"eng"}],"doi":"10.1016/j.jde.2018.07.045","arxiv":1,"day":"05","language":[{"iso":"eng"}],"publication":"Journal of Differential Equations","month":"01","oa_version":"Preprint","status":"public","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","main_file_link":[{"url":"https://arxiv.org/abs/1408.1587","open_access":"1"}],"date_published":"2019-01-05T00:00:00Z","type":"journal_article","publist_id":"7770","oa":1},{"acknowledgement":"The work of the author is supported by F.R.S.-FNRS ( Fonds de la Recherche Scientifique - FNRS ) through a Research Fellowship.\r\n\r\n","volume":35,"isi":1,"external_id":{"arxiv":["1607.00268"],"isi":["000437975500005"]},"date_updated":"2023-09-19T10:39:09Z","year":"2018","citation":{"ama":"Duerinckx M, Fischer JL. Well-posedness for mean-field evolutions arising in superconductivity. <i>Annales de l’Institut Henri Poincare (C) Non Linear Analysis</i>. 2018;35(5):1267-1319. doi:<a href=\"https://doi.org/10.1016/j.anihpc.2017.11.004\">10.1016/j.anihpc.2017.11.004</a>","apa":"Duerinckx, M., &#38; Fischer, J. L. (2018). Well-posedness for mean-field evolutions arising in superconductivity. <i>Annales de l’Institut Henri Poincare (C) Non Linear Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.anihpc.2017.11.004\">https://doi.org/10.1016/j.anihpc.2017.11.004</a>","chicago":"Duerinckx, Mitia, and Julian L Fischer. “Well-Posedness for Mean-Field Evolutions Arising in Superconductivity.” <i>Annales de l’Institut Henri Poincare (C) Non Linear Analysis</i>. Elsevier, 2018. <a href=\"https://doi.org/10.1016/j.anihpc.2017.11.004\">https://doi.org/10.1016/j.anihpc.2017.11.004</a>.","ieee":"M. Duerinckx and J. L. Fischer, “Well-posedness for mean-field evolutions arising in superconductivity,” <i>Annales de l’Institut Henri Poincare (C) Non Linear Analysis</i>, vol. 35, no. 5. Elsevier, pp. 1267–1319, 2018.","short":"M. Duerinckx, J.L. Fischer, Annales de l’Institut Henri Poincare (C) Non Linear Analysis 35 (2018) 1267–1319.","mla":"Duerinckx, Mitia, and Julian L. Fischer. “Well-Posedness for Mean-Field Evolutions Arising in Superconductivity.” <i>Annales de l’Institut Henri Poincare (C) Non Linear Analysis</i>, vol. 35, no. 5, Elsevier, 2018, pp. 1267–319, doi:<a href=\"https://doi.org/10.1016/j.anihpc.2017.11.004\">10.1016/j.anihpc.2017.11.004</a>.","ista":"Duerinckx M, Fischer JL. 2018. Well-posedness for mean-field evolutions arising in superconductivity. Annales de l’Institut Henri Poincare (C) Non Linear Analysis. 35(5), 1267–1319."},"abstract":[{"text":"We establish the existence of a global solution for a new family of fluid-like equations, which are obtained in certain regimes in as the mean-field evolution of the supercurrent density in a (2D section of a) type-II superconductor with pinning and with imposed electric current. We also consider general vortex-sheet initial data, and investigate the uniqueness and regularity properties of the solution. For some choice of parameters, the equation under investigation coincides with the so-called lake equation from 2D shallow water fluid dynamics, and our analysis then leads to a new existence result for rough initial data.","lang":"eng"}],"arxiv":1,"doi":"10.1016/j.anihpc.2017.11.004","day":"01","page":"1267-1319","quality_controlled":"1","publisher":"Elsevier","author":[{"full_name":"Duerinckx, Mitia","last_name":"Duerinckx","first_name":"Mitia"},{"first_name":"Julian L","last_name":"Fischer","orcid":"0000-0002-0479-558X","full_name":"Fischer, Julian L","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87"}],"issue":"5","_id":"606","scopus_import":"1","title":"Well-posedness for mean-field evolutions arising in superconductivity","intvolume":"        35","publication_status":"published","date_created":"2018-12-11T11:47:27Z","article_processing_charge":"No","department":[{"_id":"JuFi"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1607.00268"}],"date_published":"2018-08-01T00:00:00Z","type":"journal_article","publist_id":"7199","oa":1,"language":[{"iso":"eng"}],"publication":"Annales de l'Institut Henri Poincare (C) Non Linear Analysis","month":"08","oa_version":"Submitted Version"},{"type":"journal_article","date_published":"2018-01-30T00:00:00Z","oa":1,"publist_id":"7425","file":[{"file_size":557338,"checksum":"89a8eae7c52bb356c04f52b44bff4b5a","date_created":"2019-11-07T12:20:25Z","content_type":"application/pdf","file_name":"2018_SIAM_Fischer.pdf","date_updated":"2020-07-14T12:46:22Z","access_level":"open_access","relation":"main_file","creator":"dernst","file_id":"6992"}],"status":"public","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","has_accepted_license":"1","publication":"SIAM Journal on Mathematical Analysis","oa_version":"Published Version","month":"01","language":[{"iso":"eng"}],"citation":{"short":"J.L. Fischer, G. Grün, SIAM Journal on Mathematical Analysis 50 (2018) 411–455.","mla":"Fischer, Julian L., and Günther Grün. “Existence of Positive Solutions to Stochastic Thin-Film Equations.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 50, no. 1, Society for Industrial and Applied Mathematics , 2018, pp. 411–55, doi:<a href=\"https://doi.org/10.1137/16M1098796\">10.1137/16M1098796</a>.","ista":"Fischer JL, Grün G. 2018. Existence of positive solutions to stochastic thin-film equations. SIAM Journal on Mathematical Analysis. 50(1), 411–455.","apa":"Fischer, J. L., &#38; Grün, G. (2018). Existence of positive solutions to stochastic thin-film equations. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics . <a href=\"https://doi.org/10.1137/16M1098796\">https://doi.org/10.1137/16M1098796</a>","ama":"Fischer JL, Grün G. Existence of positive solutions to stochastic thin-film equations. <i>SIAM Journal on Mathematical Analysis</i>. 2018;50(1):411-455. doi:<a href=\"https://doi.org/10.1137/16M1098796\">10.1137/16M1098796</a>","chicago":"Fischer, Julian L, and Günther Grün. “Existence of Positive Solutions to Stochastic Thin-Film Equations.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics , 2018. <a href=\"https://doi.org/10.1137/16M1098796\">https://doi.org/10.1137/16M1098796</a>.","ieee":"J. L. Fischer and G. Grün, “Existence of positive solutions to stochastic thin-film equations,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 50, no. 1. Society for Industrial and Applied Mathematics , pp. 411–455, 2018."},"year":"2018","date_updated":"2023-09-11T13:59:22Z","external_id":{"isi":["000426630900015"]},"isi":1,"day":"30","doi":"10.1137/16M1098796","abstract":[{"text":"We construct martingale solutions to stochastic thin-film equations by introducing a (spatial) semidiscretization and establishing convergence. The discrete scheme allows for variants of the energy and entropy estimates in the continuous setting as long as the discrete energy does not exceed certain threshold values depending on the spatial grid size $h$. Using a stopping time argument to prolongate high-energy paths constant in time, arbitrary moments of coupled energy/entropy functionals can be controlled. Having established Hölder regularity of approximate solutions, the convergence proof is then based on compactness arguments---in particular on Jakubowski's generalization of Skorokhod's theorem---weak convergence methods, and recent tools on martingale convergence.\r\n\r\n","lang":"eng"}],"volume":50,"ddc":["510"],"scopus_import":"1","_id":"404","issue":"1","author":[{"first_name":"Julian L","last_name":"Fischer","orcid":"0000-0002-0479-558X","full_name":"Fischer, Julian L","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Grün","first_name":"Günther","full_name":"Grün, Günther"}],"date_created":"2018-12-11T11:46:17Z","article_processing_charge":"No","department":[{"_id":"JuFi"}],"publication_status":"published","intvolume":"        50","title":"Existence of positive solutions to stochastic thin-film equations","quality_controlled":"1","page":"411 - 455","file_date_updated":"2020-07-14T12:46:22Z","publisher":"Society for Industrial and Applied Mathematics ","article_type":"original"},{"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","status":"public","volume":159,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1703.00730"}],"abstract":[{"text":"We establish a weak–strong uniqueness principle for solutions to entropy-dissipating reaction–diffusion equations: As long as a strong solution to the reaction–diffusion equation exists, any weak solution and even any renormalized solution must coincide with this strong solution. Our assumptions on the reaction rates are just the entropy condition and local Lipschitz continuity; in particular, we do not impose any growth restrictions on the reaction rates. Therefore, our result applies to any single reversible reaction with mass-action kinetics as well as to systems of reversible reactions with mass-action kinetics satisfying the detailed balance condition. Renormalized solutions are known to exist globally in time for reaction–diffusion equations with entropy-dissipating reaction rates; in contrast, the global-in-time existence of weak solutions is in general still an open problem–even for smooth data–, thereby motivating the study of renormalized solutions. The key ingredient of our result is a careful adjustment of the usual relative entropy functional, whose evolution cannot be controlled properly for weak solutions or renormalized solutions.","lang":"eng"}],"publist_id":"6975","oa":1,"doi":"10.1016/j.na.2017.03.001","day":"01","publication_identifier":{"issn":["0362546X"]},"date_published":"2017-08-01T00:00:00Z","type":"journal_article","date_updated":"2021-01-12T08:11:55Z","citation":{"ista":"Fischer JL. 2017. Weak–strong uniqueness of solutions to entropy dissipating reaction–diffusion equations. Nonlinear Analysis: Theory, Methods and Applications. 159, 181–207.","short":"J.L. Fischer, Nonlinear Analysis: Theory, Methods and Applications 159 (2017) 181–207.","mla":"Fischer, Julian L. “Weak–Strong Uniqueness of Solutions to Entropy Dissipating Reaction–Diffusion Equations.” <i>Nonlinear Analysis: Theory, Methods and Applications</i>, vol. 159, Elsevier, 2017, pp. 181–207, doi:<a href=\"https://doi.org/10.1016/j.na.2017.03.001\">10.1016/j.na.2017.03.001</a>.","chicago":"Fischer, Julian L. “Weak–Strong Uniqueness of Solutions to Entropy Dissipating Reaction–Diffusion Equations.” <i>Nonlinear Analysis: Theory, Methods and Applications</i>. Elsevier, 2017. <a href=\"https://doi.org/10.1016/j.na.2017.03.001\">https://doi.org/10.1016/j.na.2017.03.001</a>.","ieee":"J. L. Fischer, “Weak–strong uniqueness of solutions to entropy dissipating reaction–diffusion equations,” <i>Nonlinear Analysis: Theory, Methods and Applications</i>, vol. 159. Elsevier, pp. 181–207, 2017.","apa":"Fischer, J. L. (2017). Weak–strong uniqueness of solutions to entropy dissipating reaction–diffusion equations. <i>Nonlinear Analysis: Theory, Methods and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.na.2017.03.001\">https://doi.org/10.1016/j.na.2017.03.001</a>","ama":"Fischer JL. Weak–strong uniqueness of solutions to entropy dissipating reaction–diffusion equations. <i>Nonlinear Analysis: Theory, Methods and Applications</i>. 2017;159:181-207. doi:<a href=\"https://doi.org/10.1016/j.na.2017.03.001\">10.1016/j.na.2017.03.001</a>"},"year":"2017","publisher":"Elsevier","language":[{"iso":"eng"}],"page":"181 - 207","quality_controlled":"1","month":"08","title":"Weak–strong uniqueness of solutions to entropy dissipating reaction–diffusion equations","intvolume":"       159","publication_status":"published","oa_version":"Submitted Version","department":[{"_id":"JuFi"}],"date_created":"2018-12-11T11:48:05Z","author":[{"last_name":"Fischer","first_name":"Julian L","full_name":"Fischer, Julian L","orcid":"0000-0002-0479-558X","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87"}],"_id":"712","publication":"Nonlinear Analysis: Theory, Methods and Applications","scopus_import":1}]