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.