Solvability theorem for a surface reaction type model

Abstract

The purpose of this paper is to investigate the existence and uniqueness of classical solutions to a model of surface reactions between two polyatomic reactants. The model is described by a coupled system of four quasilinear parabolic equations where two of them are determined in the domain and the other two are considered on a part of its surface. The elliptic operators of the parabolic equations determined on the surface are allowed to be degenerate in the sense that the density-dependent diffusion coefficients pi(θi) may have the property pi(1)=0, i=1,2.