JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (2): 75-87.doi: 10.6040/j.issn.1671-9352.0.2024.255

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Existence of pullback attactors for wave equations with time dependent coefficients

ZHAI Zhao, ZHANG Ping, MA Qiaozhen*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2026-02-13

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Abstract: This paper is concerned with the nonlinear wave equations with time-dependent coefficients. Firstly, the well-posedness of the solution is proved based on the theory of the uniform sector operator. Secondly, the bounded dissipation of the process is obtained by constructing appropriate functionals. Finally, the asymptotic compactness of the process is proved by using the method of the compression function. In the research of the problem, since the time-dependent coefficients α1 are decomposed into positive and negative parts, the operator decomposition technique cannot be applied when proving the asymptotic compactness of the process. Therefore, the method of compressing the function is chosen.

Key words: contractive function, well-posedness, pullback attractors, time-dependent coefficients, dissipation, compactness

CLC Number: 

  • O175
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