Differential Equations

, Volume 54, Issue 1, pp 106–120 | Cite as

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

Partial Differential Equations

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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© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Matrosov Institute for System Dynamics and Control Theory, Siberian BranchRussian Academy of SciencesIrkutskRussia

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