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

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 ca...

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Bibliographic Details
Published in:Differential equations 2018, Vol.54 (1), p.106-120
Main Authors: Kosov, A. A., Semenov, E. I.
Format: Article
Language:English
Subjects:
Anisotropy
Difference and Functional Equations
Differential equations
Diffusion
Exact solutions
Mathematics
Mathematics and Statistics
Nonlinear equations
Nonlinear systems
Ordinary Differential Equations
Partial Differential Equations
Reaction-diffusion equations
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Summary: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.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266118010093