2015/12/16 by Jean‐Michel Coron, Coron, Jean-Michel, Sylvain Ervedoza +7
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations
paper · doi:10.48550/arxiv.1512.05151
openalex publication_date 2015/12/16 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
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].