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On Exact Multidimensional Solutions of a Nonlinear System of Reaction–Diffusion Equations

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Abstract

We study a nonlinear reaction–diffusion system modeled by a system of two parabolic-type equations with power-law nonlinearities. Such systems describe the processes of nonlinear diffusion in reacting two-component media. We construct multiparameter families of exact solutions and distinguish the cases of blow-up solutions and exact solutions periodic in time and anisotropic in spatial variables that can be represented in elementary functions.

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Authors and Affiliations

  1. Matrosov Institute for System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, Irkutsk, 664033, Russia

    A. A. Kosov & E. I. Semenov

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  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 © A.A. Kosov, E.I. Semenov, 2018, published in Differentsial’nye Uravneniya, 2018, Vol. 54, No. 1, pp. 108–122.

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Kosov, A.A., Semenov, E.I. On Exact Multidimensional Solutions of a Nonlinear System of Reaction–Diffusion Equations. Diff Equat 54, 106–120 (2018). https://doi.org/10.1134/S0012266118010093

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  • DOI: https://doi.org/10.1134/S0012266118010093

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