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SIAMMA
2010

Nonlinear Cross-Diffusion with Size Exclusion

13 years 5 months ago
Nonlinear Cross-Diffusion with Size Exclusion
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. Key words. diffusion, size exclusion, cross-diffusion, ion channels, large-time behavior AMS subject classifications. 35K65, 35K51, 35Q92, 92C37, 35B40 DOI. 10.1137/100783674
Martin Burger, Marco Di Francesco, Jan-Frederik Pi
Added 21 May 2011
Updated 21 May 2011
Type Journal
Year 2010
Where SIAMMA
Authors Martin Burger, Marco Di Francesco, Jan-Frederik Pietschmann, Bärbel Schlake
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