On a class of solutions of the Krook-Tjon-Wu model of the Boltzmann equation

Abstract

The construction of the solutions of the Krook-Wu model of the nonlinear Boltzmann equation (elastic differential cross sections inversely proportional to the relative speed of the colliding particles) is reduced to the resolution of a nonlinear first order differential system for functions which are related to the moments of the Boltzmann distribution functions. These functions depend upon only one variable, the time, and are the coefficients in the Laguerre expansion of the Tjon-Wu distribution function. We explicitly show how to construct the solutions of the nonlinear differential system and study the properties of the corresponding Tjon-Wu distribution function. Show more