ON WEAK AND STRONG-CONVERGENCE TO EQUILIBRIUM FOR SOLUTIONS TO THE LINEAR BOLTZMANN-EQUATION

This paper considers the linear space-inhomogeneous Boltzmann equation for a distribution function in a bounded domain with general boundary conditions together with an external potential force. The paper gives results on strong convergence to equilibrium, when t --> infinity, for general initial data; first in the cutoff case, and then for infinite-range collision forces. The proofs are based on the properties of translation continuity and weak convergence to equilibrium. To handle these problems general H-theorems (concerning monotonicity in time of convex entropy functionals) are presented. Furthermore, the paper gives general results on collision invariants, i.e., on functions satisfying detailed balance relations in a binary collision.