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arXiv · 1403.5881

Group analysis of the Fourier transform of the spatially homogeneous and isotropic Boltzmann equation with a source term

A. Suriyawichitseranee·Yu. N. Grigoriev·S. V. Meleshko
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Abstract

The paper is devoted to group analysis of the spatially homogeneous and isotropic Boltzmann equation with a source term. In fact, the Fourier transform of the Boltzmann equation with respect to the molecular velocity variable is considered. Using a particular class of solutions, the determining equation for the admitted Lie group is reduced to a partial differential equation for the source function. The latter equation is analyzed by an algebraic method. A complete group classification of the Fourier transform of the Boltzmann equation is given. All invariant solutions of this equation are also presented in the paper.

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A. Suriyawichitseranee, Yu. N. Grigoriev, S. V. Meleshko. 2014-03-24. Group analysis of the Fourier transform of the spatially homogeneous and isotropic Boltzmann equation with a source term. https://doi.org/10.1016/j.cnsns.2014.06.047

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