MICHAEL BOEHM, I. G. ROSEN
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
Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976)

MSC:

35Q80 Applications of PDE in areas other than physics

35K45 Initial value problems for pararabolic systems

35K57 Reaction-diffusion equations

35R35 Free boundary problems for PDE

35D05 Existence of generalized solutions

35K60 Nonlinear boundary value problems for linear parabolic PDE; boundary value problems for nonlinear parabolic PDE

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.
Keywords: moving boundary problem, quasilinear systems, reaction-diffusion equations, well-posedness, maximum estimates, porous media, corrosion, one-dimensional