THE MULTIDIMENSIONAL WAVE EQUATION WITH GENERALIZED ACOUSTIC BOUNDARY CONDITIONS I: STRONG STABILITY

被引：23

作者：

Abbas, Z. ^{[1
]}

Nicaise, S. ^{[1
]}

机构：

[1] Univ Valenciennes & Hainaut Cambresis, Inst Sci & Tech Valenciennes, Lab Math & Ses Applicat Valenciennes, FR CNRS 2956, F-59313 Le Mt Houy 9, Valenciennes, France

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2015年 / 53卷 / 04期

关键词：

wave equation; acoustic boundary conditions; stability; STABILIZATION; DECAY; ENERGY;

D O I：

10.1137/140971336

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We study the wave equation on a domain of R-d, d >= 2, with dynamical boundary control applied on a part of the boundary and a Dirichlet boundary condition on the remaining part. We prove the asymptotic stability and nonuniform stability of the associated semigroup.

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页码：2558 / 2581

页数：24

相关论文

共 24 条

[1] THE MULTIDIMENSIONAL WAVE EQUATION WITH GENERALIZED ACOUSTIC BOUNDARY CONDITIONS II: POLYNOMIAL STABILITY [J].

Abbas, Z. ;

Nicaise, S. .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2015, 53 (04) :2582-2607

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

ARENDT, W ;

BATTY, CJK .

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

[3] SHARP SUFFICIENT CONDITIONS FOR THE OBSERVATION, CONTROL, AND STABILIZATION OF WAVES FROM THE BOUNDARY [J].

BARDOS, C ;

LEBEAU, G ;

RAUCH, J .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1992, 30 (05) :1024-1065

[4] LONG-TERM STABILITY ANALYSIS OF ACOUSTIC ABSORBING BOUNDARY CONDITIONS [J].

Barucq, Helene ;

Diaz, Julien ;

Duprat, Veronique .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2013, 23 (11) :2129-2154

[5] SPECTRAL PROPERTIES OF AN ACOUSTIC BOUNDARY-CONDITION [J].

BEALE, JT .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1976, 25 (09) :895-917

[6]

Belinsky BP, 2000, INT SOC ANAL APP COM, V7, P1319

[7] Optimal polynomial decay of functions and operator semigroups [J].

Borichev, Alexander ;

Tomilov, Yuri .

MATHEMATISCHE ANNALEN, 2010, 347 (02) :455-478

[8]

Brezis H., 1983, COLLECT MATH APPL

[9] SPECTRAL THEORY FOR CONTRACTION SEMIGROUPS ON HILBERT-SPACE [J].

GEARHART, L .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1978, 236 (FEB) :385-394

[10]

Grisvard P., 1985, MONOGR STUD MATH, V24