Abstract
We generalize known results on transport equations associated to a Lipschitz field \({\fancyscript {F}}\) 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 ∂Ω generalizing known results from [9],[16]. 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.
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Arlotti, L., Banasiak, J. & Lods, B. A New Approach to Transport Equations Associated to a Regular Field: Trace Results and Well-posedness. Mediterr. J. Math. 6, 367 (2009). https://doi.org/10.1007/s00009-009-0022-7
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DOI: https://doi.org/10.1007/s00009-009-0022-7