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.
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
\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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https://www.mathnet.ru/eng/nano1
https://www.mathnet.ru/eng/nano/v8/i1/p5
This publication is cited in the following 4 articles:
Alisher Matyakubov, Dilmurod Raupov, NOVEL TRENDS IN RHEOLOGY IX, 2997, NOVEL TRENDS IN RHEOLOGY IX, 2023, 020055
Z. R. Rakhmonov, J. E. Urunbaev, A. A. Alimov, INTERNATIONAL CONFERENCE ON ACTUAL PROBLEMS OF APPLIED MECHANICS - APAM-2021, 2637, INTERNATIONAL CONFERENCE ON ACTUAL PROBLEMS OF APPLIED MECHANICS - APAM-2021, 2022, 040008
Alisher Matyakubov, Dilmurod Raupov, Lecture Notes in Civil Engineering, 180, Technological Advancements in Construction, 2022, 289
Zafar R. Rakhmonov, Jasur E. Urunbayev, “Ob odnoi zadache kross-diffuzii s nelokalnymi granichnymi usloviyami”, Zhurn. SFU. Ser. Matem. i fiz., 12:5 (2019), 614–620
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