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.
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The authors were supported by the Russian Science Foundation (Grant no. 22–29–00819).
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Translated from Sibirskii Matematicheskii Zhurnal, 2022, Vol. 63, No. 6, pp. 1290–1307. https://doi.org/10.33048/smzh.2022.63.610
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Kosov, A.A., Semenov, E.I. New Exact Solutions of the Diffusion Equation with Power Nonlinearity. Sib Math J 63, 1102–1116 (2022). https://doi.org/10.1134/S0037446622060106
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DOI: https://doi.org/10.1134/S0037446622060106