Nonlinear cross-diffusion with size exclusion

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

Research output: Contribution to journalArticle

48 Citations (Scopus)

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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Cross-diffusion
Existence of Weak Solutions
Large Time Behavior
Continuum Model
Strong Solution
Behavior of Solutions
Degeneracy
Well-posedness
Global Existence
Term
Model

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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

Nonlinear cross-diffusion with size exclusion. / Burger, M.; Di Francesco, Marco; Pietschmann, J.-F.; Schlake, B.

In: SIAM Journal on Mathematical Analysis (SIMA), Vol. 42, No. 6, 2010, p. 2842-2871.

Research output: Contribution to journalArticle

Burger, M, Di Francesco, M, Pietschmann, J-F & Schlake, B 2010, 'Nonlinear cross-diffusion with size exclusion', SIAM Journal on Mathematical Analysis (SIMA), vol. 42, no. 6, pp. 2842-2871. https://doi.org/10.1137/100783674
Burger, M. ; Di Francesco, Marco ; Pietschmann, J.-F. ; Schlake, B. / Nonlinear cross-diffusion with size exclusion. In: SIAM Journal on Mathematical Analysis (SIMA). 2010 ; Vol. 42, No. 6. pp. 2842-2871.
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