Existence and asymptotic stability of a periodic solution with boundary layers of reaction-diffusion equations with singularly perturbed Neumann boundary conditions

Abstract

We consider singularly perturbed reaction-diffusion equations with singularly perturbed Neumann boundary conditions. We establish the existence of a time-periodic solution u(x; t; epsilon) with boundary layers and derive conditions for their asymptotic stability The boundary layer part of u(x; t; ") is of order one, which distinguishes our case from the case of regularly perturbed Neumann boundary conditions, where the boundary layer is of order epsilon.