Global existence of solutions of a strongly coupled quasilinear parabolic system with applications to electrochemistry

This paper consists of two parts. In the first part, we proved the global existence of weak solutions of a strongly coupled quasilinear parabolic system in Rn using weak compactness method. In the second part, we considered the electrochemistry model studied in Choi and Lui (J. Differential Equations 116 (1995) 306) where the Poisson equation governing the electric potential is replaced by a local electro-neutrality condition. In one space dimension, the equations for the model is of the form considered in the first part of this paper except that the coefficient matrix is discontinuous at places where all the charged ions vanish. We approximate the equations by nicer operators and pass to the limit to obtain global existence of weak solutions. The non-negativity of weak solutions and L2-stability of the steady-state solutions are also shown under additional hypotheses.