Michael Boehm, I.G. Rosen
Global Weak Solution and Well-Posedness of Weak Solutions for a Moving Boundary Problem for a Coupled System of Diffusion-Reaction Equations arising in the Corrosion Modelling of Concrete (Part 2)
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

35B30 Dependence of solutions of PDE on initial and boundary data, parameters, See also {58F14}

35B50 Maximum principles

Abstract: The evolution of the corrosion interface separating the uncorroded concrete part and the corroded part of a partially wet concrete wall of a pipe under the influence of hydrogen sulfide can be modelled by a moving boundary problem for three coupled one-dimensional diffusion equations. We show that the problem formulated via weak solutions is well-posed. The function describing the position of the moving boundary belongs to $W^{1,\infty}(\R^+)$. The paper generalizes previous results by relaxing the assumptions and by providing global weak solutions instead of local ones.
Keywords: moving boundary problem, system of reaction-diffusion equations, well-posedness, maximum estimates, one-dimensional, porous media, corrosion