On Solutions to the Linear Boltzmann Equation with Inelastic Granular Collisions and Infinite Range Forces

摘要

This paper considers the time- and space-dependent linear Boltzmann equation with general boundary conditions in the case of inelastic (granular) collisions. First, in the angular cut-off case, mild L l -solutions are constructed as limits of iterate functions, and boundedness of higher velocity moments are studied in the case of inverse power collision forces. Then the problem with inelastic collisions in the infinite range case (without cut-oft) will be studied in an integral weak form, combining methods from our earlier papers, and using an H-theorem for a relative entropy functional.