Nonlinear Cross-Diffusion with Size Exclusion

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

Research output: Contribution to journalArticlepeer-review

59 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

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