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 in:Siberian mathematical journal 2022, Vol.63 (6), p.1102-1116
Main Authors: Kosov, A. A., Semenov, E. I.
Format: Article
Language:English
Subjects:
Diffusion
Exact solutions
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinearity
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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