On global boundedness of higher velocity moments for solutions to the linear Boltzmann equation with hard sphere collisions

This paper considers the time- and space-dependent linear Boltzmann equation for elastic or inelastic (granular) collisions. First, in the angular cut-off case or with hard sphere collisions, mild L 1-solutions are constructed as limits of iterate functions. Then, in the case of hard sphere collisions together with, e.g., specular boundary conditions, global boundedness in time of higher velocity moments is proved, using our old collision velocity estimates together with a Jensen inequality. This generalizes our earlier results for hard inverse collision forces, and also results given by other authors from the space-homogeneous case to our space-dependent one