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On application of kinetic formulation of the Le Roux system

Part of: Hyperbolic equations and systems Partial differential equations

Published online by Cambridge University Press:  02 February 2009

Zhixin Cheng
Zhixin Cheng
Affiliation:
Department of Mathematics, University of Science and Technology of China, 230026 Hefei, Anhui, People's Republic of China ([email protected])
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Abstract

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We use the compensated compactness method coupled with some basic ideas of kinetic formulation developed by Lions, Perthame, Souganidis and Tadmor to give a refined proof for the existence of global bounded entropy solutions to the Le Roux system. This new method of the reduction of Young measures can be applied to solve other problems.

Keywords

strong entropyentropy solutionhyperbolic systemkinetic formulation

MSC classification

Secondary: 35L65: Conservation laws 35B45: A priori estimates 35L45: Initial value problems for first-order hyperbolic systems
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 1 , February 2009 , pp. 263 - 272
Copyright
Copyright © Edinburgh Mathematical Society 2009