Exact Solutions of the Nonlinear Diffusion Equation
- Authors: Kosov A.A.1, Semenov È.I.1
-
Affiliations:
- Matrosov Institute of Systems Dynamics and Control Theory
- Issue: Vol 60, No 1 (2019)
- Pages: 93-107
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/172213
- DOI: https://doi.org/10.1134/S0037446619010117
- ID: 172213
Cite item
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.
About the authors
A. A. Kosov
Matrosov Institute of Systems Dynamics and Control Theory
Author for correspondence.
Email: kosov_idstu@mail.ru
Russian Federation, Irkutsk
È. I. Semenov
Matrosov Institute of Systems Dynamics and Control Theory
Author for correspondence.
Email: edwseiz@gmail.com
Russian Federation, Irkutsk