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In this study, we consider a system of degenerate reaction-diffusionequations, which govern the electric activity in the heart with a diffusionterm modeling the potential in the surrounding tissue and the nonlinear ionicmodel proposed by Morris $\&$ Lecar. The global existence of a solution isestablished based on regularization argument using Fedo-Galerkin/Compactnessapproach. The uniqueness of the solution is shown based on Gronwell's Lemmaupon some special treatment of nonlinear terms. The system of the continuousspace-time model is first reduced to a semi-discrete time-dependent systembased on finite element formulation, and then the fully discrete system isderived using the Backward Euler time stepping scheme. The numerical solutionobtained using FreeFem++ are presented.

On the existence-uniqueness and computation of solution of a coupled PDE-ODE system with application to cardiac electric activity