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Article Dans Une Revue Journal of Differential Equations Année : 2017

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

Résumé

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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hal-01244280 , version 1 (15-12-2015)

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Jean-Michel Coron, Sylvain Ervedoza, Shyam Sundar 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, 2017, 262, pp.1-30. ⟨hal-01244280⟩
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