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On transport equations driven by a non‐divergence‐free force field |
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| Authors: | L Arlotti J Banasiak B Lods |
| Institution: | 1. Dipartimento di Ingegneria Civile, Università di Udine, via delle Scienze 208, Udine 33100, Italy;2. School of Mathematical Sciences, University of KwaZulu‐Natal, Durban 4041, South AfricaSchool of Mathematical Sciences, University of KwaZulu‐Natal, Durban 4041, South Africa===;3. Laboratoire de Mathématiques, CNRS UMR 6620, Université Blaise Pascal (Clermont‐Ferrand 2), Aubière Cedex 63177, France |
| Abstract: | The paper is devoted to initial boundary value problems for transport equations with non‐divergence‐free external field. The crucial role is played by integration along characteristics and associated Green's formula for which we provide a new proof which generalizes and clarifies previous versions. The paper concludes with an application of general theory to the Spencer–Lewis equation. Copyright © 2007 John Wiley & Sons, Ltd. |
| Keywords: | boundary‐value problem for transport equation non‐divergence‐free field characteristic curves |