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.

中文翻译：

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3 维域中具有非局部弱阻尼和超三次非线性的波动方程的长期动力学，第二部分：非自治情况

在本文中，我们研究了有界光滑域\(\mathbb {R}^3.\)中具有非局部弱阻尼和超三次非线性的非自治波动方程的长期动力学。在有界域的情况下，我们首先证明 Shatah-Struwe 解的全局适定性。然后我们建立了均匀\(\varphi \)吸引子的概念，并验证了Shatah-Struwe解过程族具有均匀多项式吸引子，它是一个紧一致吸引集，并且以多项式速度吸引任意有界子集。