Article ID Journal Published Year Pages File Type
5024592 Nonlinear Analysis: Theory, Methods & Applications 2017 18 Pages PDF
Abstract
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 L2 control. The heart of our proof is a semi-implicit scheme tailored for cross-diffusion systems firstly defined in Desvillettes et al. (2015) and a (nonlinear Aubin-Lions type) compactness result developed in Moussa (2016) and Andreianov et al. (2015) that turns the (potentially weak) gradient estimates into almost everywhere convergence. We apply our results to models having an entropy relying on the detailed balance condition exhibited by Chen et. al. in Chen et al. (2016).
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Physical Sciences and Engineering Engineering Engineering (General)
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