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Sibirskii Matematicheskii Zhurnal, 2015, Volume 56, Number 4, Pages 805–820
DOI: https://doi.org/10.17377/smzh.2015.56.408 (Mi smj2680) 		 
Multidimensional exact solutions of a nonlinear system of two parabolic equations

A. A. Kosov, E. I. Semenov

Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, Irkutsk, Russia
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DOI: https://doi.org/10.17377/smzh.2015.56.408
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.
Keywords: parabolic equation, nonlinear system, multidimensional exact solution.
Received: 07.07.2014
English version:
Siberian Mathematical Journal, 2015, Volume 56, Issue 4, Pages 637–649
DOI: https://doi.org/10.1134/S0037446615040084
Bibliographic databases:
Document Type: Article
UDC: 517.946
Language: Russian
Citation: A. A. Kosov, E. I. Semenov, “Multidimensional exact solutions of a nonlinear system of two parabolic equations”, Sibirsk. Mat. Zh., 56:4 (2015), 805–820; Siberian Math. J., 56:4 (2015), 637–649
Citation in format AMSBIB
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