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

Athmane Bakhta (1) , Virginie Ehrlacher (2, 1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 MATHERIALS - MATHematics for MatERIALS

This note focuses on some issues for the analysis of a system of degenerate cross-diffusion partial differential equations (PDEs). This family of model s are encountered in a wide variety of contexts, such as population dynamics, biology, chemistry or materials science. The application we have in mind here is the modeling of the evolution of the concentration of chemical species composing a crystalline solid. The functions, that are the solutions of the system of PDEs of interest, represent the local densities of the different components of the material, and thus should be nonnegative, bounded and satisfy some volumic constraints which will be made precise later in the note. These systems are useful for instance for the prediction of the chemical composition of thin solid films grown by Chemical Vapor Deposition (CVD). In this process, a solid wafer is exposed to gaseous precursors, corresponding to the different species entering the composition of the film, which react or decompose on the substrate surface to produce the desired deposit. This process generally occurs at high temperature and takes several hours, so that the diffusion of the different atomic species within the bulk of the solid has to be taken into account in addition to the evolution of the surface of the film.

Domaines: Mathématiques [math]

Athmane Bakhta, Virginie Ehrlacher. Global existence of bounded weak solutions to degenerate cross-diffusion equations in moving domain. ESAIM: Mathematical Modelling and Numerical Analysis, In press. ⟨hal-01238636⟩