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Zh. Vychisl. Mat. Mat. Fiz., 2005, Volume 45, Number 11, Pages 2044–2051 (Mi zvmmf571)  

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

Approximate solutions to a nonlinear heat conduction problem

N. A. Kudryashov

Moscow Engineering Physics Institute (State University), Kashirskoe sh. 31, Moscow, 115409, Russia

Abstract: A nonlinear heat conduction problem on a half-line is examined. It is assumed that the temperature at the medium boundary varies with time according to a power or exponential law and that the initial temperature of the medium is zero. An approximate solution to the problem is obtained. Exact solutions are found in special cases. The convergence of the solutions found is discussed.

Key words: radiant heat conduction, nonlinear heat equation, gas filtration, approximate solutions, exact solutions.

Full text: PDF file (869 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2005, 45:11, 1965–1972

Bibliographic databases:

Document Type: Article
UDC: 519.633.6
Received: 06.09.2004

Citation: N. A. Kudryashov, “Approximate solutions to a nonlinear heat conduction problem”, Zh. Vychisl. Mat. Mat. Fiz., 45:11 (2005), 2044–2051; Comput. Math. Math. Phys., 45:11 (2005), 1965–1972

Citation in format AMSBIB
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\by N.~A.~Kudryashov
\paper Approximate solutions to a nonlinear heat conduction problem
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2005
\vol 45
\issue 11
\pages 2044--2051
\mathnet{http://mi.mathnet.ru/zvmmf571}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2203227}
\zmath{https://zbmath.org/?q=an:1109.35059}
\transl
\jour Comput. Math. Math. Phys.
\yr 2005
\vol 45
\issue 11
\pages 1965--1972


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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. N. A. Kudryashov, M. A. Chmykhov, “Approximate solutions to one-dimensional nonlinear heat conduction problems with a given flux”, Comput. Math. Math. Phys., 47:1 (2007), 107–117  mathnet  crossref  mathscinet  zmath
    2. Stepanova I.V., “Group Classification for Equations of Thermodiffusion in Binary Mixture”, Commun. Nonlinear Sci. Numer. Simul., 18:6 (2013), 1341–1346  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Kudryashov N.A. Kochanov M.B. Savatorova V.L., “Approximate Self-Similar Solutions for the Boundary Value Problem Arising in Modeling of Gas Flow in Porous Media with Pressure Dependent Permeability”, Appl. Math. Model., 37:7 (2013), 5563–5573  crossref  mathscinet  isi  elib  scopus
    4. I. V. Kudinov, O. Yu. Kurganova, V. K. Tkachev, “Poluchenie tochnogo analiticheskogo resheniya statsionarnoi dvumernoi zadachi teploprovodnosti s istochnikom teploty”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 23:1 (2019), 195–203  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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