Energy estimates for delay diffusion-reaction equations

Abstract

In this paper we consider nonlinear delay diffusion-reaction equations with initial and Dirichlet boundary conditions. The behavior and the stability of the solution of such initial boundary value problems (IBVPs) are studied using energy method. Simple numerical methods are considered on the computation of numerical approximations to the solution of the nonlinear IBVPs. Using the discrete energy method we study the behavior of the numerical approximations, its stability and its convergence. Numerical experiments illustrating the theoretical results established are also included.