An \(L^p\)-approach to the well-posedness of transport equations associated to a regular field. II. (English) Zbl 1427.47015
Summary: This work represents the continuation of Part I [the authors, ibid. 16, No. 6, Paper No. 152, 25 p. (2019; Zbl 1427.47016)]. In \(L^p\)-spaces \(1< p <\infty\), we investigate the well-posedness of transport equations with general external Lipschitz fields and general measures associated to a large variety of boundary conditions modelled by abstract boundary operators \(H\). In particular, a new explicit formula for the corresponding transport semigroup is given. Some applications are also presented.
MSC:
| 47D06 | One-parameter semigroups and linear evolution equations |
| 35F05 | Linear first-order PDEs |
| 82C70 | Transport processes in time-dependent statistical mechanics |
Citations:
Zbl 1427.47016References:
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