On Boundedness of Higher Velocity Moments for the Linear Boltzmann Equation with Diffuse Boundary Conditions

Abstract

This article 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 potentials together with diffuse boundary conditions, global boundedness in time of higher velocity moments is proved, using our old collision velocity estimates together with a Jensen inequality.

Keywords:

• Linear Boltzmann equation
• hard potential collisions
• higher velocity moments