In this paper, we consider the weakly damped wave equations with hereditary effects and the nonlinearity $ f $ satisfying sup-cubic growth. Based on the recent extension of the Strichartz estimates to the case of bounded domains, we establish the global well-posedness of the Shatah-Struwe solutions for the non-autonomous case. Then, we prove the existence of the pullback $ \mathcal{D} $-attractors in $ C_{H_{0}^{1}(\Omega)}\times C_{L^{2}(\Omega)} $ for the solutions process $ \{U(t,\tau)\}_{t\geq\tau} $ by applying the idea of contractive functions.

中文翻译：

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具有时滞和超三次非线性的弱阻尼波动方程的回拉吸引子

在本文中，我们考虑具有遗传效应的弱阻尼波动方程和满足超三次增长的非线性$ f $。基于最近将Strichartz估计扩展到有界域的情况，我们为非自治情况建立了Shatah-Struwe解的全局适定性。然后，我们证明了$ C_ {H_ {0} ^ {1}（\ Omega）} \ x C_ {L ^ {2}（\ Omega）} $中存在回撤$ \ mathcal {D} $的吸引子解决方案通过应用压缩函数的思想来处理$ \ {U（t，\ tau）\} _ {t \ geq \ tau} $。