3D-streaming operator with multiplying boundary conditions: semigroup generation properties

In the present paper, we face a very general, but physically consistent, situation: a three dimensional (3D) bounded convex domain with regular surface, where the boundary conditions are introduced only in abstract sense by means of a cut-off operator, which is suitably defined through its properties and which represents any kind of possible linear boundary condition. The results known in literature concern the cases that we define as dissipative and conservative ones. Here we investigate the case of multiplying boundary conditions, for which we prove that the streaming operator generates a quasi-bounded C_0 semigroup .