Stability of the transmission plate equation with a delay term in the moment feedback control

被引：0

作者：

Ghecham, Wassila ^{[1
]}

Rebiai, Salah-Eddine ^{[1
]}

Sidiali, Fatima Zohra ^{[1
]}

机构：

[1] Univ Batna 2, LTM, Batna, Algeria

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2021年 / 44卷 / 09期

关键词：

boundary stabilization; Euler-Bernoulli plate equation; time delay; transmission problem; WAVE-EQUATION; BOUNDARY; STABILIZATION;

D O I：

10.1002/mma.6572

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the stability problem for the transmission plate equation with moment feedback control that contains a delay term and that acts on the exterior boundary. We prove under some assumptions that the closed-loop system is exponentially stable. To establish this result, we introduce a suitable energy function and use multipliers method and compactness-uniqueness argument.

引用

页码：7676 / 7692

页数：17

共 12 条

[1] Ammari K., 2009, Cubo, V11, P39
[2] Interior Feedback Stabilization of Wave Equations with Dynamic Boundary Delay
Ammari, Kais
Gerbi, Stephane
[J]. ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2017, 36 (03): : 297 - 327
[3] Exponential stability for a coupled system of damped-undamped plate equations
Denk, Robert
Kammerlander, Felix
[J]. IMA JOURNAL OF APPLIED MATHEMATICS, 2018, 83 (02) : 302 - 322
[4] Hassine F, 2013, ARXIV13013536V5
[5] Logarithmic stabilization of the Euler Bernoulli transmission plate equation with locally distributed Kelvin-Voigt damping
Hassine, Fathi
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 455 (02) : 1765 - 1782
[6] ASYMPTOTIC-BEHAVIOR WITH RESPECT TO THICKNESS OF BOUNDARY STABILIZING FEEDBACK FOR THE KIRCHOFF PLATE
HORN, MA
LASIECKA, I
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1994, 114 (02) : 396 - 433
[7] Ji G, 1998, OPTIMAL CONTROL THEO, V15, P224
[8] SHARP TRACE ESTIMATES OF SOLUTIONS TO KIRCHHOFF AND EULER-BERNOULLI EQUATIONS
LASIECKA, I
TRIGGIANI, R
[J]. APPLIED MATHEMATICS AND OPTIMIZATION, 1993, 28 (03) : 277 - 306
[9] Stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks
Nicaise, Serge
Pignotti, Cristina
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2006, 45 (05) : 1561 - 1585
[10] Uniform exponential stability of the transmission wave equation with a delay term in the boundary feedback
Rebiai, S. E.
Ali, F. Z. Sidi
[J]. IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION, 2016, 33 (01) : 1 - 20

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