Nonlinear Cross-Diffusion with Size Exclusion

Martin Burger, Marco Di Francesco, Jan-Frederik Pietschmann, Bärbel Schlake

Research output: Contribution to journalArticlepeer-review

86 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)2842-2871
Number of pages30
JournalSIAM Journal on Mathematical Analysis
Volume42
Issue number6
DOIs
StatePublished - Jan 2010
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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