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

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

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.

Sergey V. Meleshko | Amornrat Suriyawichitseranee | Yurii N. Grigoriev

[1] On group classification of the spatially homogeneous and isotropic Boltzmann equation with sources II , 2012 .

[2] G. Spiga,et al. Global solution to a nonlinear integral evolution problem in particle transport theory , 1982 .

[3] Yurii N. Grigoriev,et al. Symmetries of Integro-Differential Equations , 2010 .

[4] A. Bobylev,et al. The Fourier transform method in the theory of the Boltzmann equation for Maxwellian molecules , 1975 .

[5] T. Wu,et al. Formation of Maxwellian Tails , 1976 .

[6] Application of the similarity method to the nonlinear Boltzmann equation , 1984 .

[7] G. Spiga,et al. Nonlinear diffusion of test particles in the presence of an external conservative force , 1982 .

[8] Sergey V. Meleshko,et al. Methods for Constructing Exact Solutions of Partial Differential Equations: Mathematical and Analytical Techniques with Applications to Engineering , 2005 .