Handle URI:
http://hdl.handle.net/10754/598987
Title:
Nonlinear Cross-Diffusion with Size Exclusion
Authors:
Burger, Martin; Di Francesco, Marco; Pietschmann, Jan-Frederik; Schlake, Bärbel
Abstract:
The aim of this paper is to investigate the mathematical properties of a continuum model for diffusion of multiple species incorporating size exclusion effects. The system for two species leads to nonlinear cross-diffusion terms with double degeneracy, which creates significant novel challenges in the analysis of the system. We prove global existence of weak solutions and well-posedness of strong solutions close to equilibrium. We further study some asymptotics of the model, and in particular we characterize the large-time behavior of solutions. 2010 © Society for Industrial and Applied Mathematics.
Citation:
Burger M, Di Francesco M, Pietschmann J-F, Schlake B (2010) Nonlinear Cross-Diffusion with Size Exclusion. SIAM J Math Anal 42: 2842–2871. Available: http://dx.doi.org/10.1137/100783674.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Mathematical Analysis
Issue Date:
Jan-2010
DOI:
10.1137/100783674
Type:
Article
ISSN:
0036-1410; 1095-7154
Sponsors:
The authors acknowledge financial support from Volkswagen Stiftung via the grant Multiscale simulation of ion transport through biological and synthetic channels. The first author was further supported by the German Science Foundation DFG via project DFG BU 3227/2-1.This author was partially supported by the KAUST Investigator Award of Peter Markowich, and by the Italian MIUR under the PRIN program "Nonlinear Systems of Conservation Laws and Fluid Dynamics."This author was partially supported by the KAUST Investigator Award of Peter Markowich, as well as by the Leverhulme Trust through the Research Grant entitled Kinetic and mean field partial differential models for socio-economic processes (PI Peter Markowich).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorBurger, Martinen
dc.contributor.authorDi Francesco, Marcoen
dc.contributor.authorPietschmann, Jan-Frederiken
dc.contributor.authorSchlake, Bärbelen
dc.date.accessioned2016-02-25T13:50:40Zen
dc.date.available2016-02-25T13:50:40Zen
dc.date.issued2010-01en
dc.identifier.citationBurger M, Di Francesco M, Pietschmann J-F, Schlake B (2010) Nonlinear Cross-Diffusion with Size Exclusion. SIAM J Math Anal 42: 2842–2871. Available: http://dx.doi.org/10.1137/100783674.en
dc.identifier.issn0036-1410en
dc.identifier.issn1095-7154en
dc.identifier.doi10.1137/100783674en
dc.identifier.urihttp://hdl.handle.net/10754/598987en
dc.description.abstractThe aim of this paper is to investigate the mathematical properties of a continuum model for diffusion of multiple species incorporating size exclusion effects. The system for two species leads to nonlinear cross-diffusion terms with double degeneracy, which creates significant novel challenges in the analysis of the system. We prove global existence of weak solutions and well-posedness of strong solutions close to equilibrium. We further study some asymptotics of the model, and in particular we characterize the large-time behavior of solutions. 2010 © Society for Industrial and Applied Mathematics.en
dc.description.sponsorshipThe authors acknowledge financial support from Volkswagen Stiftung via the grant Multiscale simulation of ion transport through biological and synthetic channels. The first author was further supported by the German Science Foundation DFG via project DFG BU 3227/2-1.This author was partially supported by the KAUST Investigator Award of Peter Markowich, and by the Italian MIUR under the PRIN program "Nonlinear Systems of Conservation Laws and Fluid Dynamics."This author was partially supported by the KAUST Investigator Award of Peter Markowich, as well as by the Leverhulme Trust through the Research Grant entitled Kinetic and mean field partial differential models for socio-economic processes (PI Peter Markowich).en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectCross-diffusionen
dc.subjectDiffusionen
dc.subjectIon channelsen
dc.subjectLarge-time behavioren
dc.subjectSize exclusionen
dc.titleNonlinear Cross-Diffusion with Size Exclusionen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Mathematical Analysisen
dc.contributor.institutionWestfalische Wilhelms-Universitat Munster, Munster, Germanyen
dc.contributor.institutionUniversita degli Studi dell'Aquila, L'Aquila, Italyen
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdomen
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