Semigroup generation properties of streaming operators with non--contractive boundary conditions

Abstract

We present $c_0$--semigroup generation results for the free streaming operator with abstract boundary conditions. We recall some known results on the matter and establish a general theorem. We motivate our study with a lot of examples and show that our result applies to the physical cases of Maxwell boundary conditions in the kinetic theory of gases as well as to the non--local boundary conditions involved in transport--like equations from population dynamics.