Preliminary group classification of the full Boltzmann equation with a source term
Abstract
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 L11 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 L11, 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.- Publication:
-
Proceedings of the XXV Conference on High-Energy Processes in Condensed Matter (HEPCM 2017)
- Pub Date:
- October 2017
- DOI:
- 10.1063/1.5007520
- Bibcode:
- 2017AIPC.1893c0062K