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《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (6): 22-29.doi: 10.6040/j.issn.1671-9352.0.2020.359

• • 上一篇    

带有强阻尼的波方程在Rn上的时间依赖吸引子

吴晓霞1,2,马巧珍1*   

  1. 1.西北师范大学数学与统计学院, 甘肃 兰州 730070;2.塔里木大学信息工程学院, 新疆 阿拉尔 843300
  • 发布日期:2021-06-03
  • 作者简介:吴晓霞(1994— ), 女, 硕士, 研究方向为无穷维动力系统. E-mail:1173166130@qq.com*通信作者简介:马巧珍(1971— ), 女, 博士,教授, 研究方向为无穷维动力系统. E-mail:maqzh@nwnu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11861057)

Time-dependent attractors of the wave equations with strong damping on Rn

WU Xiao-xia1,2, MA Qiao-zhen1*   

  1. 1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China;
    2. College of Information Engineering, Tarim University, Alaer 843300, Xinjiang, China
  • Published:2021-06-03

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摘要： 基于尾部估计技巧和(Ct)条件获得了与研究问题相关的过程的渐近紧性,克服了全空间中Sobolev嵌入不紧和 Poincaré不等式不成立的困难,从而证明了无界域上具有强阻尼和衰退系数的波方程时间依赖吸引子的存在性。

关键词: 波方程, 强阻尼, (Ct)条件, 无界域, 时间依赖吸引子

Abstract: Based on the tail estimation technique and condition (Ct), the asymptotic compactness of the process related to the problem is obtained, and the difficulty of Sobolev embedding noncompactness and Poincaré inequality is not established in the entire space is overcome, thus the existence of time-dependent attractors for the wave equations with strong damping and decay coefficients over unbounded domains is proved.

Key words: wave equations, strong damping, condition (Ct), unbounded domain, time-dependent attractors

中图分类号: 

  • O175.27
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