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Transactions of the American Mathematical Society

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Analysis of a coupled system of kinetic equations and conservation laws: Rigorous derivation and existence theory via defect measures


Author: M. Tidriri
Journal: Trans. Amer. Math. Soc. 357 (2005), 2133-2164
MSC (2000): Primary 35L65, 82B40
Published electronically: January 21, 2005
MathSciNet review: 2140435
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Abstract: In this paper we introduce a coupled system of kinetic equations of B.G.K. type and then study its hydrodynamic limit. We obtain as a consequence the rigorous derivation and existence theory for a coupled system of kinetic equations and their hydrodynamic (conservation laws) limit. The latter is a particular case of the coupled system of Boltzmann and Euler equations. A fundamental element in this study is the rigorous derivation and justification of the interface conditions between the kinetic model and its hydrodynamic conservation laws limit, which is obtained using a new regularity theory introduced herein.


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Additional Information

M. Tidriri
Affiliation: Department of Mathematics, Iowa State University, Ames, Iowa 50011-2064
Email: tidriri@iastate.edu

DOI: https://doi.org/10.1090/S0002-9947-05-03830-4
Received by editor(s): January 17, 2003
Published electronically: January 21, 2005
Additional Notes: The author was partially supported by the Air Force Office of Scientific Research under Grant F49620-99-1-0197.
Article copyright: © Copyright 2005 American Mathematical Society