On boundary control of a hyperbolic system with a vanishing characteristic speed

¹ School of Mathematics, Shandong University, Jinan, Shandong 250100, P.R. China
² Sorbonne Universités, UPMC University Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France
³ School of Mathematical Sciences, Fudan University, Shanghai 200433. P.R. China
hu@ann.jussieu.fr; hul10@fudan.edu.cn
⁴ School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai 200433, P.R. China
wzq@fudan.edu.cn

Received: 19 October 2014
Revised: 28 April 2015

Abstract

Despite of the fact that distributed (internal) controls are usually used to obtain controllability for a hyperbolic system with vanishing characteristic speeds, this paper is, however, devoted to study the case where only boundary controls are considered. We first prove that the system is not (null) controllable in finite time. Next, we give a sufficient and necessary condition for the asymptotic stabilization of the system under a natural feedback.