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Long-Time Dynamics of the Wave Equation with Nonlocal Weak Damping and Super-Cubic Nonlinearity in 3-D Domains, Part II: Nonautonomous Case

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Abstract

In this paper, we study the long-time dynamics for the nonautonomous wave equation with nonlocal weak damping and super-cubic nonlinearity in a bounded smooth domain of \(\mathbb {R}^3.\) Based on the Strichartz estimates for the case of bounded domains, we first prove the global well-posedness of the Shatah–Struwe solutions. Then we establish the the concept of uniform \(\varphi \)-attractor and verify that the family of Shatah–Struwe solution processes has a uniform polynomial attractor, which is a compact uniformly attracting set and attracts any bounded subsets at a polynomial speed.

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Acknowledgements

We sincerely thank Dr. Xiangming Zhu for her contribution to the establishment of new concepts in Sect. 5. This work was supported by the National Science Foundation of China Grant (Grant No. 11731005).

Funding

Funding was provided by National Natural Science Foundation of China (Grant No. 11731005).

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, 210093, Jiangsu, People’s Republic of China

    Senlin Yan, Chengkui Zhong & Zhijun Tang

  2. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Xiangming Zhu

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  1. Senlin Yan
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  2. Xiangming Zhu
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Correspondence to Xiangming Zhu.

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Yan, S., Zhu, X., Zhong, C. et al. Long-Time Dynamics of the Wave Equation with Nonlocal Weak Damping and Super-Cubic Nonlinearity in 3-D Domains, Part II: Nonautonomous Case. Appl Math Optim 88, 69 (2023). https://doi.org/10.1007/s00245-023-10043-z

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