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Sibirskii Matematicheskii Zhurnal, 2022, Volume 63, Number 6, Pages 1290–1307
DOI: https://doi.org/10.33048/smzh.2022.63.610 (Mi smj7732) 		 
This article is cited in 2 scientific papers (total in 2 papers)

New exact solutions of the diffusion equation with power nonlinearity

A. A. Kosov, È. I. Semenov

Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, Irkutsk
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DOI: https://doi.org/10.33048/smzh.2022.63.610
Abstract: We consider the multidimensional nonlinear diffusion equation with a power coefficient. Using some multidimensional quadratic ansatz, we seek for generalized automodel solutions and find new exact solutions in elementary and special functions in case of various exponents. We distinguish the events that the solutions are radially symmetric or spatially anisotropic and exhibit a series of examples demonstrating the novelty of the solutions.
Keywords: nonlinear diffusion equation, exact solution, generalized automodel solution.
Funding agency Grant number
Russian Science Foundation 22-29-00819
The authors were supported by the Russian Science Foundation (Grant no. 22–29–00819).
Received: 25.01.2022
Revised: 25.01.2022
Accepted: 15.04.2022
English version:
Siberian Mathematical Journal, 2022, Volume 63, Issue 6, Pages 1102–1116
DOI: https://doi.org/10.1134/S0037446622060106
Document Type: Article
UDC: 517.946
MSC: 35R30
Language: Russian
Citation: A. A. Kosov, È. I. Semenov, “New exact solutions of the diffusion equation with power nonlinearity”, Sibirsk. Mat. Zh., 63:6 (2022), 1290–1307; Siberian Math. J., 63:6 (2022), 1102–1116
Citation in format AMSBIB
\Bibitem{KosSem22}
\by A.~A.~Kosov, \`E.~I.~Semenov
\paper New exact solutions of the diffusion equation with power nonlinearity
\jour Sibirsk. Mat. Zh.
\yr 2022
\vol 63
\issue 6
\pages 1290--1307
\mathnet{http://mi.mathnet.ru/smj7732}
\crossref{https://doi.org/10.33048/smzh.2022.63.610}
\transl
\jour Siberian Math. J.
\yr 2022
\vol 63
\issue 6
\pages 1102--1116
\crossref{https://doi.org/10.1134/S0037446622060106}
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