On Preliminary Group Classification of the Isotropic Boltzmann Equation with a Source Term in a Problem of Homogeneous Relaxation by Using Extended Equivalence Group

Abstract

The paper is devoted to preliminary group classification 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. The equivalence transformations considered earlier were extended by the change of time. This extends the set of source functions. The analysis of the extended equivalence group is given. Using optimal systems of finite-dimensional subalgebras of these extended equivalence set of transformations, preliminary classification of the source function is obtained.