On multi-species diffusion with size exclusion
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2883 | |
dc.contributor.author | Hopf, Katharina | |
dc.contributor.author | Burger, Martin | |
dc.date.accessioned | 2022-07-05T14:28:47Z | |
dc.date.available | 2022-07-05T14:28:47Z | |
dc.date.issued | 2021 | |
dc.description.abstract | We revisit a classical continuum model for the diffusion of multiple species with size-exclusion constraint, which leads to a degenerate nonlinear cross-diffusion system. The purpose of this article is twofold: first, it aims at a systematic study of the question of existence of weak solutions and their long-time asymptotic behaviour. Second, it provides a weak-strong stability estimate for a wide range of coefficients, which had been missing so far. In order to achieve the results mentioned above, we exploit the formal gradient-flow structure of the model with respect to a logarithmic entropy, which leads to best estimates in the full-interaction case, where all cross-diffusion coefficients are non-zero. Those are crucial to obtain the minimal Sobolev regularity needed for a weak-strong stability result. For meaningful cases when some of the coefficients vanish, we provide a novel existence result based on approximation by the full-interaction case. | eng |
dc.description.version | publishedVersion | eng |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/9601 | |
dc.identifier.uri | https://doi.org/10.34657/8639 | |
dc.language.iso | eng | |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | |
dc.relation.doi | https://doi.org/10.20347/WIAS.PREPRINT.2883 | |
dc.relation.issn | 2198-5855 | |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | |
dc.subject.other | Cross diffusion | eng |
dc.subject.other | size exclusion | eng |
dc.subject.other | volume filling | eng |
dc.subject.other | gradient-flow structure | eng |
dc.subject.other | degenerate nonlinear mobility | eng |
dc.subject.other | weak-strong stability | eng |
dc.subject.other | large-data weak solutions | eng |
dc.subject.other | long-time asymptotics | eng |
dc.subject.other | relative entropy | eng |
dc.subject.other | convexity | eng |
dc.title | On multi-species diffusion with size exclusion | eng |
dc.type | Report | eng |
dc.type | Text | eng |
dcterms.extent | 24 S. | |
tib.accessRights | openAccess | |
wgl.contributor | WIAS | |
wgl.subject | Mathematik | |
wgl.type | Report / Forschungsbericht / Arbeitspapier |
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