Nonlinear cross-diffusion with size exclusion
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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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.
|Creators||Burger, M., Di Francesco, M., Pietschmann, J.-F. and Schlake, B.|
|Departments||Faculty of Science > Mathematical Sciences|
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