A new H²-norm Lyapunov function for the stability of a singularly perturbed system of two conservation laws

摘要

In this paper a class of singularly perturbed system of conservation laws is considered. The partial differential equations are equipped with boundary conditions which may be studied to derive the exponential stability. Lyapunov stability technique is used to derive sufficient conditions for the exponential stability of this system. A Lyapunov function in H²-norm for a singularly perturbed system of conservation laws is constructed. It is based on the Lyapunov functions of two subsystems in L²-norm.