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

Luisa Arlotti·Jacek Banasiak·Bertrand Lods
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Abstract

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.

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Luisa Arlotti, Jacek Banasiak, Bertrand Lods. 2009-01-24. A new approach to transport equations associated to a regular field: trace results and well-posedness. https://arxiv.org/abs/math/0610808

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