Dissipative Boundary Conditions for One-Dimensional Nonlinear Hyperbolic Systems

We give a new sufficient condition on the boundary conditions for the exponential stability of one-dimensional nonlinear hyperbolic systems on a bounded interval. Our proof relies on the construction of an explicit strict Lyapunov function. We compare our sufficient condition with other known sufficient conditions for nonlinear and linear one-dimensional hyperbolic systems. Key words. nonlinear hyperbolic systems, boundary conditions, stability, Lyapunov function AMS subject classifications. 35F30, 35F25, 93D20, 93D30

• Type: Journal
• Year: 2008
• Where: SIAMCO
• Authors: Jean-Michel Coron, Georges Bastin, Brigitte d'Andréa-Novel
• Keywords: Boundary Conditions, Nonlinear Hyperbolic Systems, SIAMCO 2008, Sufficient Conditions