Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

The relative entropy method for the stability of intermediate shock waves; the rich case

Pages: 4569 - 4577, Volume 36, Issue 8, August 2016      doi:10.3934/dcds.2016.36.4569

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Denis Serre - UMPA, ENS-Lyon 46, allée d'Italie 69364 LYON Cedex 07, France (email)
Alexis F. Vasseur - Department of Mathematics, University of Texas at Austin, 1 University Station – C1200, Austin, TX 78712-0257, United States (email)

Abstract: M.-J. Kang and one of us [2] developed a new version of the relative entropy method, which is efficient in the study of the long-time stability of extreme shocks. When a system of conservation laws is rich, we show that this can be adapted to the case of intermediate shocks.

Keywords:  Shock waves, hyperbolic conservation laws, rich systems, stability, entropy method.
Mathematics Subject Classification:  35L65, 35L67.

Received: April 2015;      Revised: August 2015;      Available Online: March 2016.