Optimal decay rate of the energy for wave equations with critical potential

被引：40
|
作者：
Ikehata, Ryo [1 ]
Todorova, Grozdena [2 ]
Yordanov, Borislav [2 ]
机构：
[1] Hiroshima Univ, Grad Sch Educ, Dept Math, Higashihiroshima 7398524, Japan
[2] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA
来源：
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN | 2013年 / 65卷 / 01期
基金：
日本学术振兴会;
关键词：
damped wave equation; critical potential; energy decay; finite speed of propagation; diffusive structure; TIME-DEPENDENT DISSIPATION; ASYMPTOTIC-BEHAVIOR; CRITICAL EXPONENT; SPACE;
D O I：
10.2969/jmsj/06510183
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the long time behavior of solutions of the wave equation with a variable damping term V(x)u(t) in the case of critical decay V(x) >= V-0(1 + vertical bar x vertical bar(2))(-1/2) (see condition (A) below). The solutions manifest a new threshold effect with respect to the size of the coefficient V-0: for 1 < V-0 < N the energy decay rate is exactly t(-V0), while for V-0 >= N the energy decay rate coincides with the decay rate of the corresponding parabolic problem.
引用
收藏
页码：183 / 236
页数：54
相关论文
共 50 条
  • [41] Energy decay for systems of semilinear wave equations with dissipative structure in two space dimensions
    Katayama, Soichiro
    Matsumura, Akitaka
    Sunagawa, Hideaki
    NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2015, 22 (04): : 601 - 628
  • [42] A new strict decay rate for systems of longitudinal m-nonlinear viscoelastic wave equations
    Bouhali, Keltoum
    Zubair, Sulima Ahmed
    Ben Khalifa, Wiem Abedelmonem Salah
    Osman, Najla ELzein AbuKaswi
    Zennir, Khaled
    AIMS MATHEMATICS, 2022, 8 (01): : 962 - 976
  • [43] Energy decay rate for a quasi-linear wave equation with localized strong dissipation
    Kim, Daewook
    Kang, Yong Han
    Lee, Mi Jin
    Jung, Il Hyo
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (01) : 164 - 172
  • [44] DECAY ESTIMATES FOR WAVE EQUATIONS WITH VARIABLE COEFFICIENTS
    Radu, Petronela
    Todorova, Grozdena
    Yordanov, Borislav
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 362 (05) : 2279 - 2299
  • [45] CONSTRUCTION OF TWO-BUBBLE SOLUTIONS FOR ENERGY-CRITICAL WAVE EQUATIONS
    Jendrej, Jacek
    AMERICAN JOURNAL OF MATHEMATICS, 2019, 141 (01) : 55 - 118
  • [46] The optimal decay rate of strong solution for the compressible Navier-Stokes equations with large initial data
    Gao, Jincheng
    Wei, Zhengzhen
    Yao, Zheng-an
    PHYSICA D-NONLINEAR PHENOMENA, 2020, 406 (406)
  • [47] Optimal energy decay rate for a class of weakly dissipative second-order systems with memory
    Munoz Rivera, Jaime E.
    Naso, Maria Grazia
    APPLIED MATHEMATICS LETTERS, 2010, 23 (07) : 743 - 746
  • [48] Optimal Time-decay Estimates for the Compressible Navier-Stokes Equations in the Critical L p Framework
    Danchin, Raphael
    Xu, Jiang
    ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2017, 224 (01) : 53 - 90
  • [49] Global well-posedness of the energy-critical stochastic nonlinear wave equations
    Brun, Enguerrand
    Li, Guopeng
    Liu, Ruoyuan
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2024, 397 : 316 - 348
  • [50] OPTIMAL DECAY ESTIMATES FOR TIME-FRACTIONAL AND OTHER NONLOCAL SUBDIFFUSION EQUATIONS VIA ENERGY METHODS
    Vergara, Vicente
    Zacher, Rico
    SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2015, 47 (01) : 210 - 239
12345