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AbstractThe 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.
CitationBurger M, Di Francesco M, Pietschmann J-F, Schlake B (2010) Nonlinear Cross-Diffusion with Size Exclusion. SIAM J Math Anal 42: 2842–2871. Available: http://dx.doi.org/10.1137/100783674.
SponsorsThe 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).