Existence and Stability of Periodic Contrast Structures in the Reaction-Advection-Diffusion Problem

摘要

A singularly perturbed periodic problem for a parabolic reaction-advection-diffusion equation at low advection is studied. The case when there is an internal transition layer under unbalanced nonlinearity is considered. An asymptotic expansion of a solution is constructed. To substantiate the asymptotics thus constructed, the asymptotic method of differential inequalities is used. The Lyapunov asymptotic stability of a periodic solution is studied; the proof uses the Krein-Rutman theorem.