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Trudy Inst. Mat. i Mekh. UrO RAN, 2012, Volume 18, Number 2, Pages 114–122 (Mi timm813)  

This article is cited in 4 scientific papers (total in 4 papers)

Application of characteristic series for constructing solutions of nonlinear parabolic equations and systems with degeneracy

A. L. Kazakov

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences

Abstract: An extension of the known method of characteristic series (A. F. Sidorov) proposed by the author earlier is used to investigate boundary value problems for a nonlinear differential equation and a nonlinear parabolic system of partial differential equations with degeneracy. New existence theorems for solutions of these problems in the class of analytic functions are proved. In particular, known solutions of the nonlinear heat equation with power dependence of thermal conductivity on temperature are generalized.

Keywords: partial differential equations, boundary value problem, existence theorem, characteristic series.

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Document Type: Article
UDC: 517.956.45
Received: 30.03.2011
Revised: 26.09.2011

Citation: A. L. Kazakov, “Application of characteristic series for constructing solutions of nonlinear parabolic equations and systems with degeneracy”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 2, 2012, 114–122

Citation in format AMSBIB
\Bibitem{Kaz12}
\by A.~L.~Kazakov
\paper Application of characteristic series for constructing solutions of nonlinear parabolic equations and systems with degeneracy
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2012
\vol 18
\issue 2
\pages 114--122
\mathnet{http://mi.mathnet.ru/timm813}
\elib{http://elibrary.ru/item.asp?id=17736191}


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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. Kazakov A.L., Lempert A.A., “Existence and Uniqueness of the Solution of the Boundary-Value Problem for a Parabolic Equation of Unsteady Filtration”, J. Appl. Mech. Tech. Phys., 54:2 (2013), 251–258  crossref  mathscinet  zmath  isi  elib  elib  scopus
    2. A. L. Kazakov, P. A. Kuznetsov, L. F. Spevak, “Ob odnoi kraevoi zadache s vyrozhdeniem dlya nelineinogo uravneniya teploprovodnosti v sfericheskikh koordinatakh”, Tr. IMM UrO RAN, 20, no. 1, 2014, 119–129  mathnet  mathscinet  elib
    3. 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
    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
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