Asymptotic-Numerical Method for Moving Fronts in Two-Dimensional R-D-A Problems

摘要

A singularly perturbed initial-boundary value problem for a parabolic equation known in applications as the reaction-diffusion equation is considered. An asymptotic expansion of the solution with moving front is constructed. Using the asymptotic method of differential inequalities we prove the existence and estimate the asymptotic expansion for such solutions. The method is based on well-known comparison theorems and formal asymptotics for the construction of upper and lower solutions in singularly perturbed problems with internal and boundary layers.