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Dissipative boundary conditions for 2 × 2 hyperbolic systems of conservation laws for entropy solutions in BV

Abstract : In this article, we investigate the BV stability of 2×2 hyperbolic systems of conservation laws with strictly positive velocities under dissipative boundary conditions. More precisely, we derive sufficient conditions guaranteeing the exponential stability of the system under consideration for entropy solutions in BV. Our proof is based on a front tracking algorithm used to construct approximate piecewise constants solutions whose BV norms are controlled through a Lyapunov functional. This Lyapunov functional is inspired by the one proposed in J. Glimm's seminal work [J. Glimm, Comm. Pure Appl. Math., 18:697--715, 1965], modified with some suitable weights in the spirit of the previous works [J.-M. Coron, G. Bastin, and B. d'Andréa Novel, SIAM J. Control Optim., 47(3):1460--1498, 2008] and [J.-M. Coron, B. d'Andréa Novel, and G. Bastin, IEEE Trans. Automat. Control, 52(1):2--11, 2007].
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https://hal.archives-ouvertes.fr/hal-01244280
Contributor : Sylvain Ervedoza <>
Submitted on : Tuesday, December 15, 2015 - 3:42:51 PM
Last modification on : Friday, March 27, 2020 - 3:54:55 AM
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  • HAL Id : hal-01244280, version 1
  • ARXIV : 1512.05151

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Jean-Michel Coron, Sylvain Ervedoza, Shyam Ghoshal, Olivier Glass, Vincent Perrollaz. Dissipative boundary conditions for 2 × 2 hyperbolic systems of conservation laws for entropy solutions in BV. Journal of Differential Equations, Elsevier, 2017, 262, pp.1-30. ⟨hal-01244280⟩

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