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

Coron, Jean-Luc; Ervedoza, Sylvain; Ghoshal, Shyam; Glass, Olivier; Perrollaz, Vincent (2017), Dissipative boundary conditions for 2 × 2 hyperbolic systems of conservation laws for entropy solutions in BV, Journal of Differential Equations, 262, 1, p. 1-30. 10.1016/j.jde.2016.09.016

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Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01244280
Date
2017
Journal name
Journal of Differential Equations
Volume
262
Number
1
Publisher
Academic Press
Pages
1-30
Publication identifier
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Author(s)
Coron, Jean-Luc
Ervedoza, Sylvain
Ghoshal, Shyam
Glass, Olivier
Perrollaz, Vincent
Abstract (EN)
In this article, we investigate the BV stability of 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 [16], modified with some suitable weights in the spirit of the previous works [9,10].
Subjects / Keywords
BV; Lyapunov functional