Nonlinear cross-diffusion with size exclusion

M. Burger, Marco Di Francesco, J.-F. Pietschmann, B. Schlake

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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.
Original languageEnglish
Pages (from-to)2842-2871
Number of pages30
JournalSIAM Journal on Mathematical Analysis (SIMA)
Volume42
Issue number6
Early online date30 Nov 2010
DOIs
Publication statusPublished - 2010

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    Burger, M., Di Francesco, M., Pietschmann, J-F., & Schlake, B. (2010). Nonlinear cross-diffusion with size exclusion. SIAM Journal on Mathematical Analysis (SIMA), 42(6), 2842-2871. https://doi.org/10.1137/100783674