STABILITY AND CONTROLLABILITY OF A WAVE EQUATION WITH DYNAMICAL BOUNDARY CONTROL

被引：5

作者：

Rao, Bopeng ^{[1
]}

Toufayli, Laila ^{[2
,3
]}

Wehbe, Ali ^{[2
,3
]}

机构：

[1] Univ Strasbourg, Inst Rech Math Avancee, F-67084 Strasbourg, France

[2] Univ Libanaise, EDST, Beirut, Lebanon

[3] Univ Libanaise, Fac Sci 1, Equipe EDP AN, Beirut, Lebanon

来源：

MATHEMATICAL CONTROL AND RELATED FIELDS | 2015年 / 5卷 / 02期

关键词：

Wave equation; dynamical control; exact controllability; polynomial decay rate; ENERGY DECAY-RATE; PLATES;

D O I：

10.3934/mcrf.2015.5.305

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, we consider the stabilization and the exact controllability of a wave equation with dynamical boundary control. We first prove the strong stability of the system and establish a polynomial decay rate for smooth solutions. We next show the exact controllability by means of a singular dynamical boundary control.

引用

页码：305 / 320

页数：16

共 21 条

[1]

[Anonymous], 1968, Problemes Aux Limites Non-Homogenes et Applications

[2]

[Anonymous], 1999, Semigroups Associated with Dissipative Systems

[3] TAUBERIAN-THEOREMS AND STABILITY OF ONE-PARAMETER SEMIGROUPS [J].

ARENDT, W ;

BATTY, CJK .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 306 (02) :837-852

[4] NOTE ON WEAK STABILIZABILITY OF CONTRACTION SEMIGROUPS [J].

BENCHIMOL, CD .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1978, 16 (03) :373-379

[5]

Brezis H, 1983, ANAL FONCTIONELLE TH

[6] UNIQUE CONTINUATION FOR ELLIPTIC-OPERATORS - A GEOMETRIC VARIATIONAL APPROACH [J].

GAROFALO, N ;

LIN, FH .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1987, 40 (03) :347-366

[7]

Huang F., 1985, Ann. Differ. Equ., V1, P43

[8]

Komornik V., 1994, Exact Controllability and Stabilization. The Multiplier Method

[9]

Lions J.-L, 1988, CONTROLABILITE EXACT, V1

[10] EXACT CONTROLLABILITY, STABILIZATION AND PERTURBATIONS FOR DISTRIBUTED SYSTEMS [J].

LIONS, JL .

SIAM REVIEW, 1988, 30 (01) :1-68

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