Global existence of bounded weak solutions to degenerate cross-diffusion equations in moving domain

2015/08/26 by Bakhta, Athmane, Ehrlacher, Virginie
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1508.06449

Abstract

The aim of this note is to present preliminary existence results for a system of cross-diffusion equations defined on a domain with moving boundaries, which model the evolution of the concentrations of different chemical species in a solid during a Chemical Vapor Deposition process. The system of equations, when the domain remains fixed over time, can be seen formally as a gradient flow system which can be analyzed using the boundedness by entropy method introduced by Burger and Jüngel. Preliminary existence results are presented in the case of a one-dimensional moving boundary domain.

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