Attractors for a Class of Abstract Evolution Equations with Fading Memory

Wang Xuan; Duan Fenxia; Hu Didi

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Attractors for a Class of Abstract Evolution Equations with Fading Memory

机译：一类具有衰落记忆的抽象演化方程的吸引子

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In this paper, we study the dynamics of an abstract evolution equation with fading memory with a critical growing nonlinearity. By use of some new methods and asymptotic estimate techniques, we first verify the asymptotic compact of solution semigroup and then prove the existence of global attractors in weak topological space and strong topological space, while the forcing term only belongs to H-1(Omega) or L-2(Omega), respectively. The results are new and appear to be optimal.

机译：在本文中，我们研究具有渐弱记忆且临界非线性增长的抽象演化方程的动力学。通过使用一些新方法和渐近估计技术，我们首先验证了溶液半群的渐近紧性，然后证明了弱拓扑空间和强拓扑空间中全局吸引子的存在，而强迫项仅属于H-1（Ω）或L-2（欧米茄）。结果是新的，似乎是最佳的。

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来源
《Mathematical Problems in Engineering》 |2017年第6期|1410408.1-1410408.16|共16页
作者
Wang Xuan; Duan Fenxia; Hu Didi;
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Northwest Normal Univ, Coll Math & Stat, Lanzhou 730070, Peoples R China;

Northwest Normal Univ, Coll Math & Stat, Lanzhou 730070, Peoples R China;

Northwest Normal Univ, Coll Math & Stat, Lanzhou 730070, Peoples R China;

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2. Strong Global Attractors for the Classical Reaction Diffusion Equations with Fading Memory [J] . WANG Xuan, DUAN Fenxia, MA Qun, Chinese journal of contemporary mathematics . 2015,第3期

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3. Global Attractors for the Classical Reaction Diffusion Equations with Fading Memory [J] . WANG Xuan, ZHU Zongwei, MA Qiaozhen Chinese journal of contemporary mathematics . 2014,第3期

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4. Kolmogorov's e-Entropyfor a Class of Invariant Sets and Dimension of Global Attractors for Second-Order Evolution Equations with Nonlinear Damping [C] . Igor Chueshov, Irena Lasiecka Conference on Control Theory for Partial Differential Equations . 2005

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6. An Inverse Problem for a Class of Conditional ProbabilityMeasure-Dependent Evolution Equations [O] . Inom Mirzaev, Erin C. Byrne, David M. Bortz -1

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7. Attractors for the nonclassical diffusion equations with fading memory [O] . Wang Xuan, Yang Lu, Zhong Chengkui 2010

机译：具有褪色记忆的非经典扩散方程的吸引子

Attractors for a Class of Abstract Evolution Equations with Fading Memory

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