DISSIPATIVE BOUNDARY CONDITIONS FOR ONE-DIMENSIONAL NONLINEAR HYPERBOLIC SYSTEMS

Jean-Michel Coron (1) , Georges Bastin (2) , Brigitte d'Andréa-Novel (3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 CSAM - Centre for Systems Engineering and Applied Mechanics
3 CAOR - Centre de Robotique

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.

Domaines: Equations aux dérivées partielles [math.AP]

Jean-Michel Coron, Georges Bastin, Brigitte d'Andréa-Novel. DISSIPATIVE BOUNDARY CONDITIONS FOR ONE-DIMENSIONAL NONLINEAR HYPERBOLIC SYSTEMS. SIAM Journal on Control and Optimization, 2008, 47 (3), pp.1460-1498. ⟨hal-00923596⟩