Existence and stability of periodic contrast structures in the reaction–advection–diffusion problem in the case of a balanced nonlinearity

Abstract

We study a singularly perturbed periodic problem for the parabolic reaction–advection–diffusion equation with small advection. We consider the case in which there exists an internal transition layer under the conditions of balanced nonlinearity. An asymptotic expansion of the solution is constructed. To substantiate this asymptotics, we use the asymptotic method of differential inequalities. The Lyapunov asymptotic stability of the periodic solution is analyzed.