Application of group analysis to the spatially homogeneous and isotropic Boltzmann equation with source using its Fourier image

Group analysis of the spatially homogeneous and molecular energy dependent Boltzmann equations with source term is carried out. The Fourier transform of the Boltzmann equation with respect to the molecular velocity variable is considered. The correspondent determining equation of the admitted Lie gr...

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Bibliographic Details
Published in:Journal of physics. Conference series 2015-06, Vol.621 (1), p.12006
Main Authors: Grigoriev, Yurii N, Meleshko, Sergey V, Suriyawichitseranee, Amornrat
Format: Article
Language:English
Subjects:
Boltzmann transport equation
Fourier transforms
Lie groups
Mathematical analysis
Partial differential equations
Physics
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Summary:Group analysis of the spatially homogeneous and molecular energy dependent Boltzmann equations with source term is carried out. The Fourier transform of the Boltzmann equation with respect to the molecular velocity variable is considered. The correspondent determining equation of the admitted Lie group is reduced to a partial differential equation for the admitted source. The latter equation is analyzed by an algebraic method. A complete group classification of the Fourier transform of the Boltzmann equation with respect to a source function is given. The representation of invariant solutions and corresponding reduced equations for all obtained source functions are also presented.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/621/1/012006