具有强阻尼和时滞的非自治板系统的拉回吸引子
Pullback Attractors for a Non-Autonomous Plate System with Strong Damping and Delay
- Inner Mongolia University of Science and Technology（内蒙古科技大学）
- Donghua University（东华大学）
- Université Le Havre Normandie（勒阿弗尔诺曼底大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文针对含时滞的非线性非自治强阻尼板方程，通过构造修正能量泛函和压缩函数法，证明了其拉回吸引子的存在性。
AI中文摘要：
本文研究一类具有时滞的非线性非自治强阻尼板方程拉回吸引子的存在性。该模型包含双调和算子、强阻尼项、非线性源项以及作用于解的历史的时滞算子。强阻尼机制与遗传时滞效应之间的相互作用在推导一致估计和证明拉回渐近紧性方面带来了若干分析上的困难。为克服这些困难，我们构造了一个适应强阻尼结构的修正能量泛函，并采用压缩函数法处理历史相空间中的时滞项。通过建立弱解的存在唯一性、一致拉回估计以及相关非自治过程的拉回渐近紧性，我们证明了具有时滞的强阻尼板方程拉回吸引子的存在性。
英文摘要：
This paper addresses the existence of pullback attractors for a class of nonlinear non-autonomous strongly damped plate equations with delay. The model contains the biharmonic operator, the strong damping term, a nonlinear source term and a delay operator acting on the history of the solution. The interaction between the strong damping mechanism and the hereditary delay effect gives rise to several analytical difficulties in deriving uniform estimates and proving pullback asymptotic compactness. To overcome these difficulties, we construct a modified energy functional adapted to the strong damping structure and employ the contractive function method to handle the delay term in the history phase space. By establishing the existence and uniqueness of weak solutions, uniform pullback estimates and the pullback asymptotic compactness of the associated non-autonomous process, we prove the existence of pullback attractors for the strongly damped plate equation with delay.
