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

• Type: Journal
• Year: 2010
• Where: SIAMMA
• Authors: Martin Burger, Marco Di Francesco, Jan-Frederik Pietschmann, Bärbel Schlake
• Keywords: Large-time Behavior, SIAMMA 2010, Size Exclusion, Size Exclusion Effects