Exact Solutions of the Boltzmann Equations with a Source
Exact solutions of a nonlinear Boltzmann kinetic equation with a source are constructed in the case of an isotropic distribution function and Maxwell model of isotropic scattering. These solutions are constructed with the use of an equivalence group such that one of its transformations uniquely identifies the class of the source functions that are linear in terms of the distribution function; moreover, the transformed equation has a zero right side. As a result, one can explicitly find invariant solutions of the type of the Bobylev-Krook-Wu solutions, in particular, those that admit physical interpretation.