Exact Solutions of the Boltzmann Equations with a Source
- Authors: Grigor’ev Y.N.1,2, Meleshko S.V.3, Suriyawichitseranee A.3
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Affiliations:
- Institute of Computational Technologies, Siberian Branch
- Novosibirsk State University
- School of Mathematics, Institute of Science
- Issue: Vol 59, No 2 (2018)
- Pages: 189-196
- Section: Article
- URL: https://journals.rcsi.science/0021-8944/article/view/160977
- DOI: https://doi.org/10.1134/S0021894418020013
- ID: 160977
Cite item
Abstract
Exact solutions of a nonlinear Boltzmann kinetic equation with a source are constructed in the case of an isotropic distribution function and Maxwell model of isotropic scattering. These solutions are constructed with the use of an equivalence group such that one of its transformations uniquely identifies the class of the source functions that are linear in terms of the distribution function; moreover, the transformed equation has a zero right side. As a result, invariant solutions of the type of the Bobylev–Krook–Wu solutions can be explicitly found, in particular, those that admit physical interpretation.
About the authors
Yu. N. Grigor’ev
Institute of Computational Technologies, Siberian Branch; Novosibirsk State University
Author for correspondence.
Email: grigor@ict.nsc.ru
Russian Federation, Novosibirsk, 630090; Novosibirsk, 630090
S. V. Meleshko
School of Mathematics, Institute of Science
Email: grigor@ict.nsc.ru
Thailand, Nakhon Ratchasima, 30000
A. Suriyawichitseranee
School of Mathematics, Institute of Science
Email: grigor@ict.nsc.ru
Thailand, Nakhon Ratchasima, 30000