Construction of Barriers for Singularly Perturbed Parabolic Problems with Cubic Nonlinearities, Taking into Account the Inflection Point

An initial-boundary value problem in a rectangle for a singularly perturbed parabolic equation with cubic nonlinearities is considered. It is assumed that the inflection point of the cubic parabola is located to the left of the root of the degenerate equation. Using the nonlinear method of corner boundary functions, a complete asymptotic expansion of the solution of the problem is constructed and its uniformity in a small parameter in the closed rectangle is proved. This paper concludes the study of singularly perturbed parabolic problems with cubic nonlinearities.