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Siberian Mathematical Journal

, Volume 60, Issue 1, pp 93–107 | Cite as

Exact Solutions of the Nonlinear Diffusion Equation

  • A. A. KosovEmail author
  • È. I. SemenovEmail author
Article
  • 11 Downloads

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 

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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Matrosov Institute of Systems Dynamics and Control TheoryIrkutskRussia

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