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

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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.

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Authors and Affiliations

  1. Institute of System Dynamics and Control Theory, Irkutsk, Russia

    E. I. Semenov

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  1. E. I. Semenov
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Original Russian Text Copyright © 2006 Semenov E. I.

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Translated from Sibirski \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Matematicheski \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Zhurnal, Vol. 47, No. 2, pp. 455–462, March–April, 2006.

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Semenov, E.I. Multidimensional exact solutions to a quasilinear parabolic equation with anisotropic heat conductivity. Sib Math J 47, 376–382 (2006). https://doi.org/10.1007/s11202-006-0049-y

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  • DOI: https://doi.org/10.1007/s11202-006-0049-y

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