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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 4, Pages 624–646 (Mi zvmmf485)  

This article is cited in 1 scientific paper (total in 1 paper)

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

N. N. Nefedova, O. E. Omel'chenkob, L. Reckec

a 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.

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

Bibliographic databases:

UDC: 519.633
Received: 31.10.2005

Citation: N. N. Nefedov, O. E. Omel'chenko, L. Recke, “Stationary internal layers in a reaction-advection-diffusion integro-differential system”, Zh. Vychisl. Mat. Mat. Fiz., 46:4 (2006), 624–646; Comput. Math. Math. Phys., 46:4 (2006), 594–615

Citation in format AMSBIB
\Bibitem{NefOmeRec06}
\by N.~N.~Nefedov, O.~E.~Omel'chenko, L.~Recke
\paper Stationary internal layers in a~reaction-advection-diffusion integro-differential system
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 4
\pages 624--646
\mathnet{http://mi.mathnet.ru/zvmmf485}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2260354}
\zmath{https://zbmath.org/?q=an:05200933}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 4
\pages 594--615
\crossref{https://doi.org/10.1134/S0965542506040087}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746068584}


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    This publication is cited in the following articles:
    1. Nefedov N.N., Nikitin A.G., Petrova M.A., Recke L., “Moving fronts in integro-parabolic reaction-advection-diffusion equations”, Differ. Equ., 47:9 (2011), 1318–1332  crossref  mathscinet  zmath  isi  elib  elib  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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