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Ufimsk. Mat. Zh., 2012, Volume 4, Issue 1, Pages 6–16 (Mi ufa127)  

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

Equivalence group analysis and nonlinear self-adjointness of the generalized Kompaneets equation

E. D. Avdonina, N. H. Ibragimov

Ufa State Aviation Technical University, Ufa, Russia

Abstract: Equivalence group analysis is applied to the Kompaneets equation. We compute the equivalence Lie algebra for the corresponding generalized Kompaneets equation. We also show that the generalized Kompaneets equation is nonlinearly self-adjoint.
The principle of an a priori use of symmetries gives a possibility to use the equivalence algebra in order to approximate the Kompaneets equation by an equation having a wider class of symmetries. Using an additional symmetry of the approximating equation and the nonlinear self-adjointness, one can construct new group invariant solutions and conservation laws.

Keywords: Kompaneets equation, generalized kompaneets equation, equivalence algebra, nonlinear self-adjointness, invariant solution.

Full text: PDF file (378 kB)
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UDC: 517.958+537.84
Received: 22.11.2011

Citation: E. D. Avdonina, N. H. Ibragimov, “Equivalence group analysis and nonlinear self-adjointness of the generalized Kompaneets equation”, Ufimsk. Mat. Zh., 4:1 (2012), 6–16

Citation in format AMSBIB
\Bibitem{AvdIbr12}
\by E.~D.~Avdonina, N.~H.~Ibragimov
\paper Equivalence group analysis and nonlinear self-adjointness of the generalized Kompaneets equation
\jour Ufimsk. Mat. Zh.
\yr 2012
\vol 4
\issue 1
\pages 6--16
\mathnet{http://mi.mathnet.ru/ufa127}


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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. Gazizov R.K., Ibragimov N.H., Lukashchuk S.Yu., “Nonlinear Self-Adjointness, Conservation Laws and Exact Solutions of Time-Fractional Kompaneets Equations”, Commun. Nonlinear Sci. Numer. Simul., 23:1-3 (2015), 153–163  crossref  mathscinet  zmath  isi  scopus
    2. S. Kovalenko, O. Patsiuk, “Lie Group Classification of the Nonlinear Generalized Kompaneets Equations With Two Functional Parameters”, J. Math. Phys., 58:8 (2017), 081506  crossref  mathscinet  zmath  isi  scopus
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