Asymptotics, Stability, and Region of Attraction of Periodic Solution to a Singularly Perturbed Parabolic Problem with Double Root of a Degenerate Equation

Abstract

For a singularly perturbed parabolic problem with Dirichlet boundary conditions, the asymptotic decomposition of a solution periodic in time and with boundary layers near the ends of the segment where the degenerate equation has a double root is constructed and substantiated. The construction algorithm for the asymptotics and the behavior of the solution in the boundary layers turn out to differ significantly as compared to the case of a simple root of a degenerate equation. The stability of the periodic solution and its region of attraction are also studied.