Asymptotic Behavior for Petrovsky Equation with Localized Damping

被引：9
|
作者：
Han, Xiaosen [1 ,2 ]
Wang, Mingxin [3 ]
机构：
[1] Henan Univ, Coll Math & Informat Sci, Kaifeng 475001, Peoples R China
[2] Southeast Univ, Dept Math, Nanjing 210018, Peoples R China
[3] Harbin Inst Technol, Ctr Sci Res, Harbin 150080, Peoples R China
来源：
ACTA APPLICANDAE MATHEMATICAE | 2010年 / 110卷 / 03期
基金：
日本学术振兴会; 中国国家自然科学基金;
关键词：
Petrovsky equation; Energy decay rate; Localized damping; ENERGY DECAY-RATES; WAVE-EQUATION; INTEGRAL-INEQUALITIES; UNIFORM DECAY; EXISTENCE; SYSTEM;
D O I：
10.1007/s10440-009-9493-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate asymptotic behavior for the solution of the Petrovsky equation with locally distributed damping. Without growth condition on the damping at the origin, we extend the energy decay result in Martinez (Rev. Math. Complut. Madr. 12(1):251-283, 1999) for the single wave equation to the Petrovsky equation. The explicit energy decay rate is established by using piecewise multiplier techniques and weighted nonlinear integral inequalities.
引用
收藏
页码：1057 / 1076
页数：20
相关论文
共 50 条
  • [1] Asymptotic Behavior for Petrovsky Equation with Localized Damping
    Xiaosen Han
    Mingxin Wang
    [J]. Acta Applicandae Mathematicae, 2010, 110 : 1057 - 1076
  • [2] Asymptotic behavior for a coupled Petrovsky and wave system with localized damping
    Wu, Zhonglin
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2013, 224 : 442 - 449
  • [3] Well-posedness and stability for a viscoelastic Petrovsky equation with a localized nonlinear damping
    Sabbagh Z.
    Khemmoudj A.
    Abdelli M.
    [J]. SeMA Journal, 2024, 81 (2) : 307 - 328
  • [4] Asymptotic behavior of a Bernoulli-Euler type equation with nonlinear localized damping
    Charao, RC
    Bisognin, E
    Bisognin, V
    Pazoto, AF
    [J]. CONTRIBUTIONS TO NONLINEAR ANALYSIS: A TRIBUTE TO D. G. DE FIGUEIREDO ON THE OCCASION OF HIS 70TH BIRTHDAY, 2006, 66 : 67 - +
  • [5] Behavior of solutions to a Petrovsky equation with damping and variable-exponent sources
    Menglan Liao
    Zhong Tan
    [J]. Science China Mathematics, 2023, 66 : 285 - 302
  • [6] On behavior of solutions to a Petrovsky equation with damping and variable-exponent sources
    Liao, Menglan
    Tan, Zhong
    [J]. SCIENCE CHINA-MATHEMATICS, 2023, 66 (02) : 285 - 302
  • [7] Behavior of solutions to a Petrovsky equation with damping and variable-exponent sources
    Menglan Liao
    Zhong Tan
    [J]. Science China Mathematics, 2023, 66 (02) : 285 - 302
  • [8] Well-posedness and stability for a Petrovsky equation with properties of nonlinear localized for strong damping
    Mohamed Braiki, Hocine
    Abdelli, Mama
    Mansouri, Sabeur
    Zennir, Khaled
    [J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (05) : 3568 - 3587
  • [9] Wellposedness and Asymptotic Behavior of the Perturbed Nonlinear Schrodinger Equation with Kerr Law Nonlinearity and Localized Damping
    Zhang, Zaiyun
    Liu, Zhenhai
    Sun, Mingbao
    [J]. FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 2020, 63 (03): : 293 - 322
  • [10] Asymptotic Behavior for a Coupled Petrovsky-Petrovsky System with Infinite Memories
    Saber, Hicham
    Ferhat, Mohamed
    Cherif, Amin Benaissa
    Blouhi, Tayeb
    Himadan, Ahmed
    Alraqad, Tariq
    Moumen, Abdelkader
    [J]. MATHEMATICS, 2023, 11 (21)
12345