This article is cited in 28 papers

Asymptotics of the front motion in the reaction-diffusion-advection problem

E. A. Antipov, N. T. Levashova, N. N. Nefedov

Lomonosov Moscow State University, Faculty of Physics

Abstract: A singularly perturbed initial boundary value problem is considered for a parabolic equation that is known in application as the reaction-diffusion-advection equation. An asymptotic expansion of solutions with a moving front is constructed. This asymptotics is proved by the method of differential inequalities, which is based on well-known comparison theorems and develops the ideas of formal asymptotics for constructing upper and lower solutions in singularly perturbed problems with internal and boundary layers.

Key words: singularly perturbed parabolic problems, reaction-diffusion-advection equations, internal layers, fronts, asymptotic methods, method of differential inequalities.

UDC: 519.633

Received: 18.11.2013
Revised: 03.03.2014

DOI: 10.7868/S0044466914100032

 English version: Computational Mathematics and Mathematical Physics, 2014, 54:10, 1536–1549

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