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Nonlocal ansatze and solutions of a nonlinear system of heat-conduction equations

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Ukrainian Mathematical Journal Aims and scope

Abstract

By a nonlocal substitution, a nonlinear system of heat-conduction equations is reduced to a scalar nonlinear heat-conduction equation. The Lie and conditional invariance of the scalar equation is used to find nonlocal ansatze which reduce the original system to systems of ordinary differential equations.

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References

  1. L. V. Ovsyannikov, “Group properties of nonlinear heat conduction equation,“Dokl. Akad. Nauk SSSR, Ser. A,125, No. 3, 492–495 (1959).

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  2. V. I. Fushchich, N. I. Serov, and T. K. Amerov, “Conditional invariance of nonlinear heat conduction equation,“Dokl. Akad. Nauk Ukrain. SSR, Ser. A, No. 11, 15–18 (1990).

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  3. V. I. Fushchich, V. M. Shtelen', and N. I. Serov,Symmetry Analysis and Exact Solutions of Nonlinear Equations in Mathematical Physics [in Russian], Naukova Dumka, Kiev (1989).

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Authors and Affiliations

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

    V. I. Fushchich (Corresponding Member, Ukrainian Academy of Sciences), N. I. Serov & T. K. Amerov

Authors
  1. V. I. Fushchich
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  2. N. I. Serov
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  3. T. K. Amerov
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 2, pp. 293–302, February, 1993.

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Fushchich, V.I., Serov, N.I. & Amerov, T.K. Nonlocal ansatze and solutions of a nonlinear system of heat-conduction equations. Ukr Math J 45, 316–327 (1993). https://doi.org/10.1007/BF01060989

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  • DOI: https://doi.org/10.1007/BF01060989

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