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Sibirskii Matematicheskii Zhurnal, 2019, Volume 60, Number 1, Pages 123–140
DOI: https://doi.org/10.33048/smzh.2019.60.111 (Mi smj3064) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Exact solutions of the nonlinear diffusion equation

A. A. Kosov, È. I. Semenov

Matrosov Institute of Systems Dynamics and Control Theory, Irkutsk, Russia
Full-text PDF (354 kB) Citations (11)
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DOI: https://doi.org/10.33048/smzh.2019.60.111
Abstract: We construct new radially symmetric exact solutions of the multidimensional nonlinear diffusion equation, which can be expressed in terms of elementary functions, Bessel functions, Jacobi elliptic functions, Lambert $W$-function, and the exponential integral. We find new self-similar solutions of a spatially one-dimensional parabolic equation similar to the nonlinear heat equation. Our exact solutions can help verify difference schemes and numerical calculations used in the mathematical modeling of processes and phenomena described by these equations.
Keywords: multidimensional nonlinear diffusion equation, nonlinear heat equation, self-similar solutions, radially symmetric exact solutions, Abel equation, Jacobi elliptic functions, Lambert $W$-function.
Received: 04.06.2018
Revised: 04.06.2018
Accepted: 17.10.2018
English version:
Siberian Mathematical Journal, 2019, Volume 60, Issue 1, Pages 93–107
DOI: https://doi.org/10.1134/S0037446619010117
Bibliographic databases:
Document Type: Article
UDC: 517.946
MSC: 35R30
Language: Russian
Citation: A. A. Kosov, È. I. Semenov, “Exact solutions of the nonlinear diffusion equation”, Sibirsk. Mat. Zh., 60:1 (2019), 123–140; Siberian Math. J., 60:1 (2019), 93–107
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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