Preliminary group classification of the full Boltzmann equation with a source term

• Main Authors: Karnbanjong, Adisak, Suriyawichitseranee, Amornrat, Grigoriev, Yurii N., Meleshko, Sergey V.
• Format: Conference Proceeding
• Language: English
• Subjects: Boltzmann transport equation; Classification; Dependent variables; Differential equations; Distribution functions; Independent variables; Invariants; Lie groups; Mathematical analysis; Rarefied gases; Representations
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/1.5007520

The classical Boltzmann equation is an integro-differential equation which describes the time evolution of rarefied gas in terms of a molecular distribution function. For some kinetic problems where it is necessary to add in the Boltzmann equation a source term depending on the independent and dependent variables. This paper is devoted to applying preliminary group classification to the Boltzmann equation with a source function by using the Lie group L 11 admitted by the classical Boltzmann equation. The developed strategy for deriving determining equation of an integro-differential equation with a source (in general form) using a known Lie group admitted by the corresponding equation without the source is applied to the Boltzmann equation with a source. Solving the determining equation for the source function for each subalgebra of the optimal system of subalgebras of the Lie algebra L 11, a preliminary group classification of the Boltzmann equation with respect to the source function is obtained. Furthermore, representations of invariant solutions of the Boltzmann equation with a source are presented. The reduced equations are also shown for some representations of invariant solutions.