Volume 22, Number 1, January-March 2016
|Page(s)||134 - 147|
|Published online||11 January 2016|
On boundary control of a hyperbolic system with a vanishing characteristic speed
School of Mathematics, Shandong University,
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
4 School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai 200433, P.R. China
Received: 19 October 2014
Revised: 28 April 2015
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.
Mathematics Subject Classification: 93B05 / 93D15 / 35L04
Key words: Hyperbolic systems / controllability / stabilization / vanishing characteristic speed / zero eigenvalue
© EDP Sciences, SMAI, 2016
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