Exponential stability of the plate equations with potential of second order and indefinite damping

被引：8
作者：
Li, Jing [1 ]
Wu, Yingtao [1 ]
机构：
[1] Sichuan Univ, Sch Math, Chengdu 610064, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2009年 / 359卷 / 01期
关键词：
Plate equation; Indefinite damping; Carleman estimate; Observability inequality; Exponential decay rate; WAVE-EQUATIONS; STABILIZATION;
D O I：
10.1016/j.jmaa.2009.05.030
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the exponential stability of the plate equations with potential of second order and indefinite sign damping term. By means of a global Carleman-type estimate and the usual perturbation method, we show that the energy of the system decays exponentially provided that the negative damping is sufficiently small. Both the energy decay rate and the upper bound estimate on the negative damping are given explicitly. (C) 2009 Elsevier Inc. All rights reserved.
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收藏
页码：62 / 75
页数：14
相关论文
共 19 条
  • [1] Decay rates of the plate equations
    Ammari, K
    Khenissi, M
    [J]. MATHEMATISCHE NACHRICHTEN, 2005, 278 (14) : 1647 - 1658
  • [2] Energy decay rate of wave equations with indefinite damping
    Benaddi, A
    Rao, BP
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2000, 161 (02) : 337 - 357
  • [3] Stability results for the wave equation with indefinite damping
    Freitas, P
    Zuazua, E
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1996, 132 (02) : 338 - 352
  • [4] Guzmán RB, 2003, SYST CONTROL LETT, V48, P191, DOI 10.1016/S0167-6911(02)00264-5
  • [5] Joly R, 2007, ASYMPTOTIC ANAL, V53, P237
  • [6] Lasiecka I., 2004, Journal of Inverse and ILL-Posed Problems, V12, P183, DOI 10.1163/1569394042530919
  • [7] Lasiecka I., 2004, J. Inverse Ill Posed Probl, V12, P43
  • [8] Lions J-L., 1988, CONTROLABILIT EXACTE
  • [9] Stabilization of the wave equations with potential and indefinite damping
    Liu, KS
    Rao, BP
    Zhang, X
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 269 (02) : 747 - 769
  • [10] Stabilization of the wave equation by on-off and positive-negative feedbacks
    Martinez, P
    Vancostenoble, J
    [J]. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2002, 7 (15): : 335 - 377
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