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Sibirskii Matematicheskii Zhurnal, 2006, Volume 47, Number 2, Pages 455–462 (Mi smj868)  
This article is cited in 1 scientific paper (total in 1 paper)

Multidimensional exact solutions to a quasilinear parabolic equation with anisotropic heat conductivity

È. I. Semenov

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences
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Abstract: We prove invariance of a quasilinear parabolic equation with anisotropic heat conductivity in the three-dimensional coordinate space under some equivalence transformations and present some explicit formulas for these transformations. We consider nontrivial reductions of the equation to similar equations of less spatial dimension. Using these results, we construct new exact multidimensional solutions to the equation which depend on arbitrary harmonic functions.
Keywords: quasilinear parabolic heat equation, Liouville equation, multidimensional exact solution, equivalence transformation, anisotropy, conjugate harmonic function.
Received: 13.01.2005
English version:
Siberian Mathematical Journal, 2006, Volume 47, Issue 2, Pages 376–382
DOI: https://doi.org/10.1007/s11202-006-0049-y
Bibliographic databases:
UDC: 517.946
Language: Russian
Citation: È. I. Semenov, “Multidimensional exact solutions to a quasilinear parabolic equation with anisotropic heat conductivity”, Sibirsk. Mat. Zh., 47:2 (2006), 455–462; Siberian Math. J., 47:2 (2006), 376–382
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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