This article is cited in 11 papers

Multidimensional exact solutions to the reaction-diffusion system with power-law nonlinear terms

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 nonlinear reaction-diffusion system that is modeled by a system of parabolic equations with power-law nonlinear terms. The proposed construction of exact solutions enables us to split the process of finding the components depending on time and the spatial coordinates. We construct multiparametric families of exact solutions in elementary functions. The cases are elaborated of blow-up solutions as well as exact solutions time-periodic but spatially anisotropic.

Keywords: reaction-diffusion system, parabolic equations, exact solutions, blow-up solutions, periodic solutions.

UDC: 517.946

MSC: 35R30

Received: 24.11.2016

DOI: 10.17377/smzh.2017.58.408

 English version: Siberian Mathematical Journal, 2017, 58:4, 619–632

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