  In this study, we consider a system of degenerate reaction-diffusion
equations, which govern the electric activity in the heart with a diffusion
term modeling the potential in the surrounding tissue and the nonlinear ionic
model proposed by Morris $\&$ Lecar. The global existence of a solution is
established based on regularization argument using Fedo-Galerkin/Compactness
approach. The uniqueness of the solution is shown based on Gronwell's Lemma
upon some special treatment of nonlinear terms. The system of the continuous
space-time model is first reduced to a semi-discrete time-dependent system
based on finite element formulation, and then the fully discrete system is
derived using the Backward Euler time stepping scheme. The numerical solution
obtained using FreeFem++ are presented.
