On periodic solutions with boundary layers in problems with nonlinear singular boundary conditions

E. I. Nikulin

Lomonosov Moscow State University

Abstract: For a reaction-diffusion problem with nonlinear singularly perturbed boundary conditions, we prove the existence and examine the stability of periodic solutions possessing boundary layers. Conditions of the asymptotic stability of these solutions in the Lyapunov sense are obtained. The proof is based on the asymptotic method of differential inequalities.

Keywords: singularly perturbed parabolic problem, nonlinear boundary condition, periodic problem, reaction-diffusion equation, boundary layer, asymptotic method, differential inequality

UDC: 517.957

MSC: 35K60

DOI: 10.36535/2782-4438-2025-243-45-55