| Autor: |
Karnbanjong, Adisak, Suriyawichitseranee, Amornrat, Grigoriev, Yurii N., Meleshko, Sergey V. |
| Rok vydání: |
2017 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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