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Multidimensional exact solutions of a nonlinear system of two parabolic equations

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Abstract

We study a system of two parabolic equations with two nonlinearities depending on the difference of the squares of unknown functions. Some conditions are found for reducibility of a system to a sole equation. The cases are distinguished in which the system can be reduced to a linear heat equation or semilinear equations. We also construct parametric families of exact solutions depending on elementary functions.

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Authors and Affiliations

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

    A. A. Kosov & E. I. Semenov

Authors
  1. A. A. Kosov
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  2. E. I. Semenov
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Correspondence to A. A. Kosov.

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Original Russian Text Copyright © 2015 Kosov A.A. and Semenov E.I.

The authors were partially supported by the Russian Foundation for Basic Research (Grant 15–08–06680), the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh–5007.2014.9), and the Interdisciplinary Project of the Siberian Division of the Russian Academy of Sciences (Grant 80).

Irkutsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 4, pp. 805–820, July–August, 2015; DOI: 10.17377/smzh.2015.56.408.

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Kosov, A.A., Semenov, E.I. Multidimensional exact solutions of a nonlinear system of two parabolic equations. Sib Math J 56, 637–649 (2015). https://doi.org/10.1134/S0037446615040084

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  • DOI: https://doi.org/10.1134/S0037446615040084

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