A STABILITY RESULT FOR A TIMOSHENKO SYSTEM WITH PAST HISTORY AND A DELAY TERM IN THE INTERNAL FEEDBACK

被引：0

作者：

Said-Houari, Belkacem ^{[1
]}

Rahali, Radouane

机构：

[1] Univ Konstanz, Dept Math & Stat, D-78457 Constance, Germany

来源：

DYNAMIC SYSTEMS AND APPLICATIONS | 2011年 / 20卷 / 2-3期

关键词：

GLOBAL EXISTENCE; WAVE-EQUATION; BOUNDARY; STABILIZATION;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider a Timoshenko system with a delay term in the feedback and memory term. Under an appropriate assumption between the weight of the delay and the weight of the damping, we prove a well posedness result. Furthermore an exponential stability result has been shown if the weight of the damping is greater or equal to the weight of the delay. We distinguish two cases: the case where the weight of the delay is less than the weight of the damping and the case where the two weights are equal. In each case we introduce an appropriate Lyapunov functional which leads to an exponential stability. This result extends the one in [15] and the recent result in [23].

引用

页码：327 / 353

页数：27

共 26 条

[1] Asymptotic behavior for Timoshenko beams subject to a single nonlinear feedback control [J].

Alabau-Boussouira, Fatiha .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2007, 14 (5-6) :643-669

[2] Energy decay for Timoshenko systems of memory type [J].

Ammar-Khodja, F ;

Benabdallah, A ;

Rivera, JEM ;

Racke, R .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2003, 194 (01) :82-115

[3] Feedback boundary stabilization of wave equations with interior delay [J].

Ammari, Kais ;

Nicaise, Serge ;

Pignotti, Cristina .

SYSTEMS & CONTROL LETTERS, 2010, 59 (10) :623-628

[4]

d L Santos M., 2002, Electron. J. Differ. Equations, V2002, P1

[5]

DAFERMOS CM, 1970, ARCH RATION MECH AN, V37, P297

[6] AN EXAMPLE ON THE EFFECT OF TIME DELAYS IN BOUNDARY FEEDBACK STABILIZATION OF WAVE-EQUATIONS [J].

DATKO, R ;

LAGNESE, J ;

POLIS, MP .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1986, 24 (01) :152-156

[7] 2 QUESTIONS CONCERNING THE BOUNDARY CONTROL OF CERTAIN ELASTIC-SYSTEMS [J].

DATKO, R .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1991, 92 (01) :27-44

[8] Ill-posed problems in thermomechanics [J].

Dreher, Michael ;

Quintanilla, Ramon ;

Racke, Reinhard .

APPLIED MATHEMATICS LETTERS, 2009, 22 (09) :1374-1379

[9] On the control of a viscoelastic damped Timoshenko-type system [J].

Guesmia, Aissa ;

Messaoudi, Salim A. .

APPLIED MATHEMATICS AND COMPUTATION, 2008, 206 (02) :589-597

[10] Stability result for the Timoshenko system with a time-varying delay term in the internal feedbacks [J].

Kirane, Mokhtar ;

Said-Houari, Belkacem ;

Anwar, Mohamed Naim .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2011, 10 (02) :667-686

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