A New Approach to Transport Equations Associated to a Regular Field: Trace Results and Well-posedness

We generalize known results on transport equations associated to a Lipschitz field F on some subspace of \mathbb{R}^N endowed with some general space measure \mu. We provide a new definition of both the transport operator and the trace measures over the incoming and outgoing parts of the boundary generalizing known results. We also prove the well-posedness of some suitable boundary-value transport problems and describe in full generality the generator of the free streaming semigroup with no-incoming boundary conditions.