JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (6): 22-29.doi: 10.6040/j.issn.1671-9352.0.2020.359

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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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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

CLC Number: 

  • O175.27
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