The Linear Boltzmann Equation with General Boundary Conditions and Infinite Range Forces
Rolf Pettersson · Operator theory · 1991
This paper considers the linear space-inhomogeneous Boltzmann equation in a convex, bounded or unbounded body D with general boundary conditions. First mild L 1 -solutions are constructed in the cut-off case using monotone sequences of iterates in an exponential form. Assuming detailed balance relations, mass conservation and uniqueness are proved, together with an H -theorem with formulas for the interior and boundary terms. Local boundedness of higher moments is proved for soft and hard collision potentials, together with global boundedness for hard potentials in the case of a non-heating boundary, including specular reflections. Next the transport equation with forces of infinite range is considered in an integral form. Existence of weak L 1 -solutions are proved by compactness, using the H -theorem from the cut-off case. Finally, an H -theorem is given also for the infinite range case. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.