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Lie symmetries and exact solutions of nonlinear equations of heat conductivity with convection term

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Abstract

The Lie symmetries of nonlinear diffusion equations with convection term are completely described. The Lie ansatzes and exact solutions of a certain nonlinear generalization of the Murray equation are constructed. An example of the family of non-Lie solutions of the Murray equation is given.

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Authors and Affiliations

  1. Poltava Technical University, Poltava

    M. I. Serov

  2. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    R. M. Cherniha

Authors
  1. M. I. Serov
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  2. R. M. Cherniha
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Translated from Ukrainskii Matematicheskii Zhurnal. Vol. 49, No. 9, pp. 1262–1270, September, 1997.

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Serov, M.I., Cherniha, R.M. Lie symmetries and exact solutions of nonlinear equations of heat conductivity with convection term. Ukr Math J 49, 1423–1433 (1997). https://doi.org/10.1007/BF02487349

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  • DOI: https://doi.org/10.1007/BF02487349

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