Exact Solutions of the Boltzmann Equations with a Source

Yu N. Grigor’ev; S. V. Meleshko; A. Suriyawichitseranee

doi:10.1134/S0021894418020013

Exact Solutions of the Boltzmann Equations with a Source

Yu N. Grigor’ev, S. V. Meleshko, A. Suriyawichitseranee

Mathematical Modeling Section

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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.

Original language	English
Pages (from-to)	189-196
Number of pages	8
Journal	Journal of Applied Mechanics and Technical Physics
Volume	59
Issue number	2
DOIs	https://doi.org/10.1134/S0021894418020013
Publication status	Published - 1 Mar 2018

Keywords

Boltzmann equation
invariant solutions
isotropic distribution function
source function

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10.1134/S0021894418020013

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AU - Grigor’ev, Yu N.

AU - Meleshko, S. V.

AU - Suriyawichitseranee, A.

PY - 2018/3/1

Y1 - 2018/3/1

N2 - 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.

AB - 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.

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KW - isotropic distribution function

KW - source function

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