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

TL;DR

This paper establishes preliminary results on the global existence of bounded weak solutions for a system of degenerate cross-diffusion equations modeling chemical species in a moving domain, relevant to chemical vapor deposition processes.

Contribution

It extends the analysis of cross-diffusion systems to moving domains, providing initial existence results using entropy methods in one dimension.

Findings

Existence of bounded weak solutions in one-dimensional moving domains.

Application of entropy methods to degenerate cross-diffusion equations.

Framework for future analysis in higher dimensions or more complex domains.

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.