Stabilization and controllability for the transmission wave equation

被引：23

作者：

Liu, WJ ^{[1
]}

机构：

[1] Dalhousie Univ, Dept Math & Stat, Halifax, NS B3H 3J5, Canada

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2001年 / 46卷 / 12期

关键词：

stabilization; transmission wave equation;

D O I：

10.1109/9.975473

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we address the problem of control of the transmission wave equation. In particular, we consider the case where, due to total internal reflection of waves at the interface, the system may not be controlled from exterior boundaries. We show that such a system can be controlled by introducing both boundary control along the exterior boundary and distributed control near the transmission boundary and give a physical explanation why the additional control near the transmission boundary might be needed for some domains.

引用

页码：1900 / 1907

页数：8

共 17 条

[1]

Adams R. A., 1975, SOBOLEV SPACES

[2]

[Anonymous], 1998, ESAIM CONTR OPTIM CA

[3] Implications of sharp trace regularity results on boundary stabilization of the system of linear elasticity [J].

Horn, MA .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 223 (01) :126-150

[4]

KOMORNIK V, 1990, J MATH PURE APPL, V69, P33

[5]

Lagnese J. E., 1997, ESAIM. Control, Optimisation and Calculus of Variations, V2, P343, DOI 10.1051/cocv:1997112

[6] UNIFORM STABILIZATION OF THE WAVE-EQUATION WITH DIRICHLET OR NEUMANN FEEDBACK-CONTROL WITHOUT GEOMETRICAL CONDITIONS [J].

LASIECKA, I ;

TRIGGIANI, R .

APPLIED MATHEMATICS AND OPTIMIZATION, 1992, 25 (02) :189-224

[7] EXPONENTIAL DECAY OF SOLUTIONS OF WAVE EQUATION IN EXTERIOR OF A STAR-SHAPED OBSTACLE [J].

LAX, PD ;

PHILLIPS, RS ;

MORAWETZ, CS .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1963, 16 (04) :477-&

[8]

Lions J. L., 1972, NONHOMOGENEOUS BOUND, VI

[9]

Lions JL., 1988, Controlabilite Exacte, Perturbation et Stabilisation de Systemes Distribues, Tome 1

[10] The exponential stabilization of the higher-dimensional linear system of thermoviscoelasticity [J].

Liu, WJ .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 1998, 77 (04) :355-386

← 1 2 →