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

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.

preprint2014arXivOpen access
A. SuriyawichitseraneeYu. N. GrigorievS. V. Meleshko
math-phmath.MP
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A. SuriyawichitseraneeYu. N. GrigorievS. V. Meleshko

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