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Matematicheskie Trudy, 2019, Volume 22, Number 2, Pages 54–75
DOI: https://doi.org/10.33048/mattrudy.2019.22.204 (Mi mt357) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Construction and investigation of exact solutions with free boundary to a nonlinear heat equation with source

A. L. Kazakov

Matrosov Institute for System Dynamics and Control Theory, Irkutsk, 664033 Russia
Full-text PDF (284 kB) Citations (5)
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DOI: https://doi.org/10.33048/mattrudy.2019.22.204
Abstract: The article is devoted to the construction and investigation of exact solutions with free boundary to a second-order nonlinear parabolic equation. The solutions belong to the classes of generalized self-similar and generalized traveling waves. Their construction is reduced to Cauchy problems for second-order ordinary differential equations (ODE), for which we prove existence and uniqueness theorems for their solutions. A qualitative analysis of the ODE is carried out by passing to a dynamical system and constructing and studying its phase portrait. In addition, we present geometric illustrations.
Key words: nonlinear heat equation with source, thermal wave, exact solution, existence theorem, qualitative analysis of ordinary differential equations.
Received: 21.11.2018
Revised: 21.11.2018
Accepted: 27.02.2019
English version:
Siberian Advances in Mathematics, 2020, Volume 30, Issue 2, Pages 91–105
DOI: https://doi.org/10.3103/S1055134420020029
Bibliographic databases:
Document Type: Article
UDC: 517.956.45+517.911
Language: Russian
Citation: A. L. Kazakov, “Construction and investigation of exact solutions with free boundary to a nonlinear heat equation with source”, Mat. Tr., 22:2 (2019), 54–75; Siberian Adv. Math., 30:2 (2020), 91–105
Citation in format AMSBIB
\Bibitem{Kaz19}
\by A.~L.~Kazakov
\paper Construction and investigation of exact solutions with free boundary to a~nonlinear heat equation with source
\jour Mat. Tr.
\yr 2019
\vol 22
\issue 2
\pages 54--75
\mathnet{http://mi.mathnet.ru/mt357}
\crossref{https://doi.org/10.33048/mattrudy.2019.22.204}
\transl
\jour Siberian Adv. Math.
\yr 2020
\vol 30
\issue 2
\pages 91--105
\crossref{https://doi.org/10.3103/S1055134420020029}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85086237855}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические труды Siberian Advances in Mathematics
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    Abstract page:316
    Full-text PDF :207
    References:43
    First page:6
     
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