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

Luisa Arlotti (1) , Jacek Banasiak (2) , Bertrand Lods (3)

1 Università degli Studi di Udine - University of Udine [Italie]
2 School of Mathematical Sciences, University of KwaZulu-Natal
3 LMBP - Laboratoire de Mathématiques Blaise Pascal

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 $\mu$. We provide a new definition of both the transport operator and the trace measures over the incoming and outgoing parts of $\partial \Omega$ 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.

Mots clés: Transport equation; Boundary conditions; $C_0$-semigroups; Characteristic curves.; Characteristic curves

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Luisa Arlotti, Jacek Banasiak, Bertrand Lods. A new approach to transport equations associated to a regular field: trace results and well-posedness.. Mediterranean Journal of Mathematics, 2009, 6 (no. 4.), pp.367--402. ⟨10.1007/s00009-009-0022-7⟩. ⟨hal-00110239v5⟩