This article is cited in 2 papers

Stationary internal layers in a reaction-advection-diffusion integro-differential system

N. N. Nefedov^a, O. E. Omel'chenko^b, L. Recke<sup>c

a</sup> Faculty of Physics, Moscow State University, Leninskie gory, Moscow, 119992, Russia
^b Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkovskaya ul. 3, Kiev, 01601, Ukraine
^c Institut für Mathematik, Humboldt Universität zu Berlin, Unter den Linden 6, Berlin, 10099, Germany

Abstract: A class of singularly perturbed nonlinear integro-differential problems with solutions involving internal transition layers (contrast structures) is considered. An asymptotic expansion of these solutions with respect to a small parameter is constructed, and the stability of stationary solutions to the associated integro-parabolic problems is investigated. The asymptotics are substantiated using the asymptotic method of differential inequalities, which is extended to the new class of problems. The method is based on well-known theorems about differential inequalities and on the idea of using formal asymptotics for constructing upper and lower solutions in singularly perturbed problems with internal and boundary layers.

Key words: singularly perturbed integro-parabolic problems, internal layers, contrast structures, differential inequalities.

UDC: 519.633

Received: 31.10.2005

 English version: Computational Mathematics and Mathematical Physics, 2006, 46:4, 594–615

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