2019/01/23 by Pargaei, Meena, Kumar, B. V. Rathish
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1901.07873
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.