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Trudy Inst. Mat. i Mekh. UrO RAN, 2014, Volume 20, Number 1, Pages 119–129 (Mi timm1035)  

This article is cited in 8 scientific papers (total in 8 papers)

On a degenerate boundary value problem for the porous medium equation in spherical coordinates

A. L. Kazakova, P. A. Kuznetsovb, L. F. Spevakc

a Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences
b Institute of Mathematics, Economics and Informatics of Irkutsk State University
c Institute of Engineering Science, Urals Branch, Russian Academy of Sciences

Abstract: We study a degenerate boundary value problem for the porous medium equation in the case of spherical coordinates. The results of this study can be applied to the problem of heat propagation in a neighborhood of a closed spherical surface. For the boundary value problem, we prove the existence and uniqueness theorem for solutions in the class of analytical functions and propose a numerical method for constructing solutions based on the boundary element approach. We use both truncated series and the proposed numerical method to carry out sample computations.

Keywords: porous medium equation, boundary value problem, analytical solution, boundary element method.

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Document Type: Article
UDC: 517.95+518.517
Received: 18.04.2013

Citation: A. L. Kazakov, P. A. Kuznetsov, L. F. Spevak, “On a degenerate boundary value problem for the porous medium equation in spherical coordinates”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 1, 2014, 119–129

Citation in format AMSBIB
\Bibitem{KazKuzSpe14}
\by A.~L.~Kazakov, P.~A.~Kuznetsov, L.~F.~Spevak
\paper On a~degenerate boundary value problem for the porous medium equation in spherical coordinates
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2014
\vol 20
\issue 1
\pages 119--129
\mathnet{http://mi.mathnet.ru/timm1035}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3364197}
\elib{http://elibrary.ru/item.asp?id=21258488}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. P. A. Kuznetsov, “O kraevoi zadache s vyrozhdeniem dlya nelineinogo uravneniya teploprovodnosti s dannymi na zamknutoi poverkhnosti”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 9 (2014), 61–74  mathnet
    2. A. L. Kazakov, P. A. Kuznetsov, A. A. Lempert, “O postroenii teplovoi volny dlya nelineinogo uravneniya teploprovodnosti v simmetrichnom sluchae”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 11 (2015), 39–53  mathnet
    3. A. L. Kazakov, L. F. Spevak, “Chislennoe i analiticheskoe issledovanie nekotorykh protsessov, opisyvaemykh nelineinym uravneniem teploprovodnosti”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 157, no. 4, Izd-vo Kazanskogo un-ta, Kazan, 2015, 42–48  mathnet  elib
    4. A. L. Kazakov, Sv. S. Orlov, “O nekotorykh tochnykh resheniyakh nelineinogo uravneniya teploprovodnosti”, Tr. IMM UrO RAN, 22, no. 1, 2016, 112–123  mathnet  mathscinet  elib
    5. A. L. Kazakov, L. F. Spevak, O. A. Nefedova, “Reshenie dvumernoi zadachi o dvizhenii fronta teplovoi volny s ispolzovaniem stepennykh ryadov i metoda granichnykh elementov”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 18 (2016), 21–37  mathnet
    6. A. L. Kazakov, P. A. Kuznetsov, “Ob analiticheskikh resheniyakh zadachi o dvizhenii teplovogo fronta dlya nelineinogo uravneniya teploprovodnosti s istochnikom”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 24 (2018), 37–50  mathnet  crossref
    7. A. L. Kazakov, P. A. Kuznetsov, “On the analytic solutions of a special boundary value problem for a nonlinear heat equation in polar coordinates”, J. Appl. Industr. Math., 12:2 (2018), 255–263  mathnet  crossref  crossref  elib  elib
    8. A. L. Kazakov, P. A. Kuznetsov, L. F. Spevak, “Trekhmernaya teplovaya volna, porozhdennaya kraevym rezhimom, zadannym na podvizhnom mnogoobrazii”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 26 (2018), 16–34  mathnet  crossref
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