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Nanosystems: Physics, Chemistry, Mathematics, 2017, Volume 8, Issue 1, Pages 5–12
DOI: https://doi.org/10.17586/2220-8054-2017-8-1-5-12 (Mi nano1) 		 
This article is cited in 4 scientific papers (total in 4 papers)

MATHEMATICS

Self-similar solutions of a cross-diffusion parabolic system with variable density: explicit estimates and asymptotic behaviour

M. M. Aripov, A. S. Matyakubov

National University of Uzbekistan, Applied Mathematics and Computer Analysis, Universitet, 4, Tashkent, 100174, Uzbekistan
Full-text PDF (287 kB) Citations (4)
DOI: https://doi.org/10.17586/2220-8054-2017-8-1-5-12
Abstract: In this paper, we study the properties of self-similar solutions of a cross-diffusion parabolic system. In particular, we find the Zeldovich–Barenblatt type solution to the cross diffusive system. The asymptotic behavior of self-similar solutions are analyzed for both the slow and fast diffusive regimes. It is shown that coefficients of the main term of the asymptotic of solution satisfy some system of nonlinear algebraic equations.
Keywords: cross-diffusive system, non-divergence form, finite speed, perturbation, global solutions, asymptotic behavior, numerical analysis.
Received: 25.07.2016
Revised: 28.08.2016
Bibliographic databases:
Document Type: Article
PACS: 02.30.Jr, 02.30.Mv, 11.10.Jj, 11.10.Lm
Language: English
Citation: M. M. Aripov, A. S. Matyakubov, “Self-similar solutions of a cross-diffusion parabolic system with variable density: explicit estimates and asymptotic behaviour”, Nanosystems: Physics, Chemistry, Mathematics, 8:1 (2017), 5–12
Citation in format AMSBIB
\Bibitem{AriMat17}
\by M.~M.~Aripov, A.~S.~Matyakubov
\paper Self-similar solutions of a cross-diffusion parabolic system with variable density: explicit estimates and asymptotic behaviour
\jour Nanosystems: Physics, Chemistry, Mathematics
\yr 2017
\vol 8
\issue 1
\pages 5--12
\mathnet{http://mi.mathnet.ru/nano1}
\crossref{https://doi.org/10.17586/2220-8054-2017-8-1-5-12}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000397241100001}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Nanosystems: Physics, Chemistry, Mathematics
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