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Trudy Inst. Mat. i Mekh. UrO RAN, 2016, Volume 22, Number 1, Pages 112–123 (Mi timm1265)  

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

On some exact solutions of the nonlinear heat equation

A. L. Kazakov, S. S. Orlov

Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, Irkutsk

Abstract: The paper is devoted to finding invariant solutions of the nonlinear heat (filter) equation without sources or sinks in the case of one spatial variable and a power dependence of the thermal conduction coefficient on the temperature. The construction procedure is reduced to Cauchy problems for ordinary differential equations with a singularity at the highest derivative. An existence and uniqueness theorem is proved for solutions of such problems in the class of analytic functions (in the form of a converging series). An estimate is obtained for the convergence domain of this series in one particular case.

Keywords: partial differential equations, nonlinear heat (filter) equation, invariant solution, Cauchy problem.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00608 А
16-31-00291 мол_а


Full text: PDF file (195 kB)
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Bibliographic databases:

Document Type: Article
UDC: 517.95
Received: 15.09.2015

Citation: A. L. Kazakov, S. S. Orlov, “On some exact solutions of the nonlinear heat equation”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 1, 2016, 112–123

Citation in format AMSBIB
\Bibitem{KazOrl16}
\by A.~L.~Kazakov, S.~S.~Orlov
\paper On some exact solutions of the nonlinear heat equation
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2016
\vol 22
\issue 1
\pages 112--123
\mathnet{http://mi.mathnet.ru/timm1265}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3497189}
\elib{http://elibrary.ru/item.asp?id=25655602}


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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. A. L. Kazakov, Sv. S. Orlov, S. S. Orlov, “Construction and study of exact solutions to a nonlinear heat equation”, Siberian Math. J., 59:3 (2018), 427–441  mathnet  crossref  crossref  isi  elib
    2. A. A. Kosov, È. I. Semenov, “Exact solutions of the nonlinear diffusion equation”, Siberian Math. J., 60:1 (2019), 93–107  mathnet  crossref  crossref  isi
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