A new approach to transport equations associated to a regular field: trace results and well-posedness

Arlotti, Luisa; Banasiak, Jacek; Lods, Bertrand

A new approach to transport equations associated to a regular field: trace results and well-posedness

Authors

Arlotti, Luisa

Banasiak, Jacek

Lods, Bertrand

Description

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