Front Motion in the Parabolic Reaction—Diffusion Problem

摘要

A singularly perturbed initial—boundary value problem is considered for a parabolic equa-tion known in applications as the reaction—diffusion equation. An asymptotic expansion of solutionswith a moving front is constructed, and an existence theorem for such solutions is proved. The asymp-totic expansion is substantiated using the asymptotic method of differential inequalities, which isextended to the class of problems under study. The method is based on well-known comparison theo-rems and is a development of the idea of using formal asymptotics for the construction of upper andlower solutions in singularly perturbed problems with internal and boundary layers.