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Article Dans Une Revue Nonlinear Analysis: Theory, Methods and Applications Année : 2017

Entropic structure and duality for multiple species cross-diffusion systems

Résumé

This paper deals with the existence of global weak solutions for a wide class of (multiple species) cross-diffusions systems. The existence is based on two different ingredients: an entropy estimate giving some gradient control and a duality estimate that gives naturally L^2 control. The proof relies on a semi-implicit scheme tailored for cross-diffusion systems firstly defined by the two authors and collaborators. These results are applied to models having an entropy relying on the detailed balance condition recently exhibited by Chen et. al.
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Dates et versions

hal-01373172 , version 1 (28-09-2016)

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Thomas Lepoutre, Ayman Moussa. Entropic structure and duality for multiple species cross-diffusion systems. Nonlinear Analysis: Theory, Methods and Applications, 2017, 159, ⟨10.1016/j.na.2017.02.008⟩. ⟨hal-01373172⟩
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