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A kinetic model for polytropic gases with internal energy |
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| Authors: | Laurent Boudin Bérénice Grec Milana Pavić-Čolić Francesco Salvarani |
| Affiliation: | 1. UPMC Univ Paris 06, UMR 7598 LJLL, Paris, F-75005, France INRIA Paris-Rocquencourt, BP 105, F-78153 Le Chesnay Cedex, France;2. MAP5, CNRS UMR 8145, Université Paris Descartes, 45 Rue des Saints Pères, F-75006 Paris, France INRIA Paris-Rocquencourt, BP 105, F-78153 Le Chesnay Cedex, France;3. Prirodno-matematički fakultet, Univerzitet u Novom Sadu, Trg Dositeja Obradovića 4, 21000 Novi Sad, Serbia;4. Dipartimento di Matematica, Università degli Studi di Pavia, I-27100, Pavia, Italy |
| Abstract: | We consider a mixture of N ideal, polytropic gases. Each species is described by a distribution function fi(t, x, v, I) ≥ 0, 1 ≤ i ≤ N, defined on  , and its evolution is governed by a Boltzmann-type equation. In order to recover the energy law of polytropic gases, the authors of [4] proposed a kinetic model in the framework of a weighted L1 space. Another approach has been developed in [3] in the context of polyatomic gases. Following this previous lead, our model provides a L2 framework in both variables v and I, to eventually perform a mathematical study of the diffusion asymptotics, as it was done in [2] for a model without energy exchange. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) |
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