Optimal decay rates for the system of elastic waves in Rn with structural damping

被引：10
|
作者：
Ikehata, Ryo [1 ]
Charao, Ruy Coimbra [2 ]
da Luz, Cleverson Roberto [2 ]
机构：
[1] Hiroshima Univ, Grad Sch Educ, Dept Math, Higashihiroshima 7398524, Japan
[2] Univ Fed Santa Catarina, Dept Math, Florianopolis, SC, Brazil
来源：
JOURNAL OF EVOLUTION EQUATIONS | 2014年 / 14卷 / 01期
关键词：
Structural damping; elastic wave equation; Fourier analysis; energy method; low frequency; high frequency; optimal decay; BOUNDARY-VALUE-PROBLEM; ENERGY DECAY; EQUATIONS;
D O I：
10.1007/s00028-014-0216-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the Cauchy problem in R (n) for the system of elastic waves with structural damping. We derive (almost) optimal decay rates in time for the L (2)-norm and the total energy which improves previous results for this system. To derive the estimates for elastic waves, we employ an improvement in a method in the Fourier space, which was developed in our previous works. Our estimates came from those for a generalized energy of alpha-order in the Fourier space.
引用
收藏
页码：197 / 210
页数：14
相关论文
共 50 条
  • [31] Rates of Decay for Porous Elastic System Weakly Dissipative
    M. L. Santos
    A. D. S. Campelo
    D. S. Almeida Júnior
    Acta Applicandae Mathematicae, 2017, 151 : 1 - 26
  • [32] OPTIMAL ENERGY DECAY RATES FOR SOME WAVE EQUATIONS WITH DOUBLE DAMPING TERMS
    Ikehata, Ryo
    Kitazaki, Shingo
    EVOLUTION EQUATIONS AND CONTROL THEORY, 2019, 8 (04): : 825 - 846
  • [33] Optimal decay estimates for the Vlasov–Poisson system with radiation damping
    Fucai Li
    Baoyan Sun
    Man Wu
    Zeitschrift für angewandte Mathematik und Physik, 2023, 74
  • [34] Decay mild solutions for elastic systems with structural damping involving nonlocal conditions
    Luong V.T.
    Tung N.T.
    Vestnik St. Petersburg University, Mathematics, 2017, 50 (1) : 55 - 67
  • [35] Existence and Decay of Solution to Coupled System of Viscoelastic Wave Equations with Strong Damping in Rn
    Bouhali, Keltoum
    Ellaggoune, Patch
    BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2021, 39 (06): : 31 - 52
  • [36] LOCAL ENERGY DECAY FOR THE ELASTIC SYSTEM WITH NONLINEAR DAMPING IN AN EXTERIOR DOMAIN
    Daoulatli, M.
    Dehman, B.
    Khenissi, M.
    SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2010, 48 (08) : 5254 - 5275
  • [37] Energy decay for a porous-elastic system with nonlinear localized damping
    Santos, M. L.
    Almeida Junior, D. S.
    Cordeiro, S. M. S.
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2022, 73 (01):
  • [38] GENERAL DECAY OF POROUS ELASTIC SYSTEM WITH THERMO-VISCOELASTIC DAMPING
    Djellali, F.
    Labidi, S.
    Taallah, F.
    EURASIAN JOURNAL OF MATHEMATICAL AND COMPUTER APPLICATIONS, 2021, 9 (01): : 31 - 43
  • [39] Energy decay for a porous-elastic system with nonlinear localized damping
    M. L. Santos
    D. S. Almeida Júnior
    S. M. S. Cordeiro
    Zeitschrift für angewandte Mathematik und Physik, 2022, 73
  • [40] Optimal Convergence Rates to Diffusion Waves for Solutions of the Hyperbolic Conservation Laws with Damping
    Pierangelo Marcati
    Ming Mei
    Bruno Rubino
    Journal of Mathematical Fluid Mechanics, 2005, 7 : S224 - S240
12345