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On General Transport Equations with Abstract Boundary Conditions. The Case of Divergence Free Force Field |
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| Authors: | Luisa Arlotti Jacek Banasiak Bertrand Lods |
| Institution: | 1. Dipartimento di Ingegneria Civile, Universit?? di Udine, via delle Scienze 208, 33100, Udine, Italy 2. School of Mathematical Sciences, University of KwaZulu?CNatal, Durban, 4041, South Africa 3. Institute of Mathematics, Technical University of ???d?, ???d?, Poland 4. Clermont Universit??, Universit?? Blaise Pascal, Laboratoire de Math??matiques, CNRS UMR 6620, BP 10448, F-63000, Clermont-Ferrand, France |
| Abstract: | This work is a continuation of our previous paper 8]. We investigate well-posedness (in the semigroup theory sense) of transport equations with general external fields and general measures associated to boundary conditions modeled by abstract boundary operators H. Fine properties of the traces are investigated, extending well-known results by M. Cessenat 15]. For dissipative boundary conditions, we revisit and generalize results from 12, 17] while, for multiplicative boundary conditions we extend techniques from 25]. Finally, we also investigate the case of boundary conditions associated to a boundary operator of norm one, extending the recent results of 6, 27] to more general fields and measures. |
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