New Exact Solutions of the Diffusion Equation with Power Nonlinearity

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 t...

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Bibliographic Details
Published inSiberian mathematical journal Vol. 63; no. 6; pp. 1102 - 1116
Main Authors Kosov, A. A., Semenov, E. I.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 2022
Springer Nature B.V
Subjects
Diffusion
Exact solutions
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinearity
nonlinear diffusion equation
exact solution
517.946
generalized automodel solution
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Summary: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.
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446622060106