Nonlinear cross-diffusion with size exclusion

Reference:

Burger, M., Di Francesco, M., Pietschmann, J.-F. and Schlake, B., 2010. Nonlinear cross-diffusion with size exclusion. SIAM Journal on Mathematical Analysis (SIMA), 42 (6), pp. 2842-2871.

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Official URL:

http://dx.doi.org/10.1137/100783674

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.

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