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Continuity Properties of Pullback and Pullback Exponential Attractors for Non-autonomous Plate with $$p-$$ Laplacian
Applied Mathematics and Optimization ( IF 1.8 ) Pub Date : 2023-11-30 , DOI: 10.1007/s00245-023-10082-6
Moncef Aouadi

Our purpose is to study some continuity properties of pullback and pullback exponential attractors for the non-autonomous plate with \(p-\)Laplacian and nonlocal weak damping \(\text {g}_\epsilon (\Vert u_t\Vert )u_t\) under hinged boundary condition. Moreover, the existence of pullback attractors in the natural space energy with finite dimensionality is proved together with its upper semicontinuity and continuity with respect to the perturbed parameter \(\epsilon \in [0, 1]\). Finally, we prove that the related process has a pullback exponential attractor \({\mathscr {M}}^\epsilon _{exp}\) and is Hölder continuous on \(\epsilon \in [0, 1]\). In particular, the continuity on perturbation \(\epsilon \in [0,1]\) holds for global and exponential attractors when the non-autonomous dynamical system degenerates to an autonomous one.



中文翻译:

具有$$p-$$拉普拉斯非自治板回拉和回拉指数吸引子的连续性

我们的目的是研究具有\(p-\)拉普拉斯和非局部弱阻尼\(\text {g}_\epsilon (\Vert u_t\Vert )u_t 的非自治板的回拉和回拉指数吸引子的一些连续性特性\)在铰接边界条件下。此外,还证明了有限维自然空间能量中回拉吸引子的存在性及其上半连续性和关于扰动参数\(\epsilon \in [0, 1]\)的连续性。最后,我们证明相关过程具有回调指数吸引子\({\mathscr {M}}^\epsilon _{exp}\)并且在\(\epsilon \in [0, 1]\)上是 Hölder 连续。特别是,当非自治动力系统退化为自治动力系统时,扰动\(\epsilon \in [0,1]\)的连续性对于全局和指数吸引子成立。

更新日期:2023-12-01
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