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

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 J\"ungel. Preliminary existence results are presented in the case of a one-dimensional moving boundary domain.