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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
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
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
Linking options:
https://www.mathnet.ru/eng/smj2680 https://www.mathnet.ru/eng/smj/v56/i4/p805
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