Global Weak Solutions and Uniqueness for a Moving Boundary Problem for a Coupled System of Quasilinear Diffusion-Reaction Equations arising as a Model of Chemical Corrosion of Concrete Surfaces

Abstract

We show existence and uniqueness for global weak solutions of a moving boundary problem for a coupled system of three quasi-linear diffusion-reaction equations. The model is briefly described. The proofs are based on Schauder's and Banach's fixed point theorems, the one-dimensional setting and they make use of relatively general and realistic assumptions on the production terms providing bounds on the weak solutions of the problem. The paper extends previously known results with constant coefficients to a quasi-linear setting.