  We consider certain Boltzmann type equations on a bounded physical and a
bounded velocity space under the presence of both, reflective as well as
diffusive boundary conditions. We introduce conditions on the shape of the
physical space and on the relation between the reflective and the diffusive
part in the boundary conditions such that the associated Knudsen type semigroup
can be extended to time $t\in\mathbb{R}$. Furthermore, we provide conditions
under which there exists a unique global solution to a Boltzmann type equation
for time $t\ge 0$ or for time $t\in [\tau_0,\infty)$ for some $\tau_0<0$ which
is independent of the initial value at time 0. Depending on the collision
kernel, $\tau_0$ can be arbitrarily small.
