留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

动态边界上随机波动方程的吸引子

杨墨 富娜

杨墨, 富娜. 动态边界上随机波动方程的吸引子[J]. 应用数学和力学, 2018, 39(9): 1068-1080. doi: 10.21656/1000-0887.380254
引用本文: 杨墨, 富娜. 动态边界上随机波动方程的吸引子[J]. 应用数学和力学, 2018, 39(9): 1068-1080. doi: 10.21656/1000-0887.380254
YANG Mo, FU Na. Attractors of Stochastic Wave Equations With Nonlinear-Damping and Dynamic Boundary Conditions[J]. Applied Mathematics and Mechanics, 2018, 39(9): 1068-1080. doi: 10.21656/1000-0887.380254
Citation: YANG Mo, FU Na. Attractors of Stochastic Wave Equations With Nonlinear-Damping and Dynamic Boundary Conditions[J]. Applied Mathematics and Mechanics, 2018, 39(9): 1068-1080. doi: 10.21656/1000-0887.380254

动态边界上随机波动方程的吸引子

doi: 10.21656/1000-0887.380254
基金项目: 国家自然科学基金(71273214);中央高校基本科研业务费(SWJTU12ZT13)
详细信息
    作者简介:

    杨墨(1991—), 男,硕士生(通讯作者. E-mail: 251160504@qq.com).

  • 中图分类号: O175; O19

Attractors of Stochastic Wave Equations With Nonlinear-Damping and Dynamic Boundary Conditions

Funds: The National Natural Science Foundation of China(71273214)
  • 摘要: 研究了一类动态边界上的随机波动方程.通过建立一种分解技术,证明了方程随机吸引子的存在性.分解同时表明,该吸引子上的点(或者解)一定满足某种稳定的边界条件.最后,证明了吸引子的结构与分解所得的静态边界上波动方程的随机吸引子相同.
  • [1] TEMAM R. Infinite-Dimensional Dynamical Systems in Mechanics and Physics [M]. New York: Springer-Verlag, 1988.
    [2] FAN X. Random attractor for a damped stochastic wave equation with multiplicative noise[J]. International Journal of Mathematics,2008,19(4): 421-437.
    [3] WANG Z, ZHOU S, GU A. Random attractor for a stochastic damped wave equation with multiplicative noise on unbounded domains[J]. Nonlinear Analysis Real World Applications,2011,12(6): 3468-3482.
    [4] ZHANG W. Maximal attractors for the m-dimensional Cahn-Hilliard system[J]. Acta Mathematica Sinica,2004,20(2): 233-246.
    [5] ZHANG W N. Dimension of maximal attractors for the m-dimensional Cahn-Hilliard system[J]. Acta Mathematica Sinica,2005,21(6): 1487-1494.
    [6] FAN Z H, ZHONG C K. Attractors for parabolic equations with dynamic boundary conditions[J]. Nonlinear Analysis Theory Methods and Applications,2008,68(6): 1723-1732.
    [7] MIRANVILLE A, ZELIK S. Exponential attractors for the Cahn-Hilliard equation with dynamic boundary conditions[J]. Mathematical Methods in the Applied Sciences,2005,28(6): 709-735.
    [8] CHUESHOV I, ELLER M, LASIECKA I. On the attractor for a semilinear wave equation with critical exponent and nonlinear boundary dissipation[J]. Communications in Partial Differential Equations,2002,27(9): 1901-1951.
    [9] WU H, ZHENG S. Convergence to equilibrium for the damped semilinear wave equation with critical exponent and dissipative boundary condition[J]. Quarterly of Applied Mathematics,2006,64(1): 167-188.
    [10] YASSINE H. Existence and asymptotic behavior of solutions to semilinear wave equations with nonlinear damping and dynamical boundary condition[J]. Journal of Dynamics & Differential Equations,2012,24(3): 645-661.
    [11] BARBU V. Nonlinear Semigroups and Differential Equations in Banach Spaces [M]. New York: Springer-Verlag, 2010.
    [12] PAZY A. Semigroups of Linear Operators and Applications to Partial Differential Equations [M]. New York: Springer-Verlag, 1983.
    [13] FRIGERI S. Attractors for semilinear damped wave equations with an acoustic boundary condition[J]. Journal of Evolution Equations,2010,10(1): 29-58.
    [14] BALL J M. Global attractors for damped semilinear wave equations[J]. Discrete & Continuous Dynamical Systems,2004,10(1): 31-52.
  • 加载中
计量
  • 文章访问数:  616
  • HTML全文浏览量:  58
  • PDF下载量:  617
  • 被引次数: 0
出版历程
  • 收稿日期:  2017-09-08
  • 修回日期:  2017-11-14
  • 刊出日期:  2018-09-15

目录

    /

    返回文章
    返回