### Karnbanjong A. Suriyawichitseranee A. Grigoriev Y.N. Meleshko S.V.

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

### Reporter: Karnbanjong A.

For some kinetic problems there is the need to include a source term depending on the independent and dependent variables into the classical Boltzmann equation.

The presentation is devoted to application of the preliminary group classification method to the Boltzmann equation with a source function by using the Lie group $L_{11}$ admitted by the classical Boltzmann equation.

The first part of the presentation gives a strategy for deriving determining equation of non-homogeneous nonlocal equation using a known Lie group admitted by the corresponding homogeneous nonlocal equation.

The second part of the presentation is devoted to application of the developed strategy 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 $L_{11}$ we obtain a preliminary group classification with respect to the source function.

The third part of the presentation provides representations of invariant solutions of Boltzmann equation with a source. The reduced equations are also shown for some representations of invariant solutions for which the collision integral can be written in new variables.

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