Exact boundary observability for a kind of second order quasilinear hyperbolic systems and its applications

Abstract

In this paper, by means of a constructive method based on the existence and uniqueness of the semi-global C 2 solution, we establish the local exact boundary observability for a kind of second order quasilinear hyperbolic systems. As an application, we obtain the one-sided local exact boundary observability for a kind of first order quasilinear hyperbolic systems of diagonal form with boundary conditions in which the diagonal variables corresponding to the positive eigenvalues and those corresponding to the negative eigenvalues are decoupled.