On boundary control of a hyperbolic system with a vanishing characteristic speed
Hu, Long1, 2, 3 ; Wang, Zhiqiang4
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
4 School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai 200433, P.R. China
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 1, pp. 134-147.

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.

Reçu le :
DOI : 10.1051/cocv/2015031
Classification : 93B05, 93D15, 35L04
Mots-clés : Hyperbolic systems, controllability, stabilization, vanishing characteristic speed, zero eigenvalue
Hu, Long 1, 2, 3 ; Wang, Zhiqiang 4

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
4 School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai 200433, P.R. China 
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Hu, Long; Wang, Zhiqiang. On boundary control of a hyperbolic system with a vanishing characteristic speed. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 1, pp. 134-147. doi : 10.1051/cocv/2015031. http://www.numdam.org/articles/10.1051/cocv/2015031/

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