Exact solutions of the Boltzmann equation

Abstract

The nonlinear Boltzmann equation for the relaxation to equilibrium of a homogeneous one‐component gas, is considered for a class of collision models. The models are characterized by elastic cross sections inversely proportional to the relative speed, but with arbitrary dependence on center‐of‐mass scattering angle. The Boltzmann equation is solved exactly for a particular family of physically interesting initial distributions. The distribution functions are of the similarity form and consist of the product of a Maxwell function with ’’time‐dependent temperature’’ and a linear function of v².