This article is cited in 11 papers

Contrast structures in the reaction-diffusion-advection equations in the case of balanced advection

N. T. Levashova, N. N. Nefedov, A. V. Yagremtsev

M. V. Lomonosov Moscow State University, Faculty of Physics

Abstract: For a singularly perturbed parabolic equation termed in applications as the reaction-diffusion-advection equation, stationary solutions with internal transition layers (contrast structures) are studied. An arbitrary-order asymptotic approximation of such solutions is constructed, and an existence theorem is proved. An efficient algorithm for constructing an asymptotic approximation of the transition point is proposed. The constructed asymptotic approximation is justified by applying the asymptotic method of differential inequalities, which is extended to the class of problems under study. This method is also used to establish the Lyapunov stability of such stationary solutions.

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

UDC: 519.63

MSC: 35K57

Received: 12.01.2012
Revised: 09.10.2012

DOI: 10.7868/S0044466913030095

 English version: Computational Mathematics and Mathematical Physics, 2013, 53:3, 273–283

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