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

7th International Workshop: Group Analysis of Differential Equations and Integrable Systems

Grigoriev, Yurii N.^1 ; Meleshko, Sergey V.^2 ; Suriyawichitseranee, Amornrat^2

Institute of Computational Technology, Novosibirsk

630090, Russia^1

School of Mathematics, Institute of Science, Suranaree University of Technology, Nakhon Ratchasima

30000, Thailand^2

关键词: Admitted Lie group;    Determining equation;    Group classification;    Invariant solutions;    Molecular energies;    Molecular velocity;    Reduced equations;    Spatially homogeneous;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/621/1/012006/pdf
DOI  :  10.1088/1742-6596/621/1/012006

来源: IOP

【 摘 要 】

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.