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J. Sib. Fed. Univ. Math. Phys., 2016, Volume 9, Issue 2, Pages 225–234 (Mi jsfu480)  

This article is cited in 2 scientific papers (total in 2 papers)

On the properties of solutions of multidimensional nonlinear filtration problem with variable density and nonlocal boundary condition in the case of fast diffusion

Zafar R. Rakhmonov

National University of Uzbekistan, 100174, University street, 4, Tashkent, Uzbekistan

Abstract: The conditions of global existence of solutions of a nonlinear filtration problem in an inhomogeneous medium are investigated in this paper. Various techniques such as the method of standard equations, self-similar analysis and the comparison principle are used to obtain results. The influence of inhomogeneous medium on the evolution process is analyzed. The critical global existence exponent and the critical Fujita exponent are obtained. Asymptotic behavior of solutions in the case of the global solvability is established.

Keywords: filtration, asymptotics, critical exponent, inhomogeneous density.

DOI: https://doi.org/10.17516/1997-1397-2016-9-2-225-234

Full text: PDF file (842 kB)
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Bibliographic databases:

UDC: 517.957
Received: 30.08.2015
Received in revised form: 04.12.2015
Accepted: 12.01.2016
Language:

Citation: Zafar R. Rakhmonov, “On the properties of solutions of multidimensional nonlinear filtration problem with variable density and nonlocal boundary condition in the case of fast diffusion”, J. Sib. Fed. Univ. Math. Phys., 9:2 (2016), 225–234

Citation in format AMSBIB
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\by Zafar~R.~Rakhmonov
\paper On the properties of solutions of multidimensional nonlinear filtration problem with variable density and nonlocal boundary condition in the case of fast diffusion
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2016
\vol 9
\issue 2
\pages 225--234
\mathnet{http://mi.mathnet.ru/jsfu480}
\crossref{https://doi.org/10.17516/1997-1397-2016-9-2-225-234}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000412008200012}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Z. R. Rakhmonov, A. I. Tillaev, “On the behavior of the solution of a nonlinear polytropic filtration problem with a source and multiple nonlinearities”, Nanosyst.-Phys. Chem. Math., 9:3 (2018), 323–329  crossref  isi
    2. Mersaid M. Aripov, Jakhongir R. Raimbekov, “The critical curves of a doubly nonlinear parabolic equation in non-divergent form with a source and nonlinear boundary flux”, Zhurn. SFU. Ser. Matem. i fiz., 12:1 (2019), 112–124  mathnet  crossref
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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