The existence of time-dependent attractors for abstract evolution equations with fading memory
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摘要: 研究了记忆型抽象发展方程在时间依赖空间上解的长时间动力学行为.运用修正的拉回吸引子理论,使用先验估计技巧和算子分解的方法验证了过程的渐近紧性,进而证明了时间依赖全局吸引子的存在性和正则性.该结果改进了一些已有结果.Abstract: In this paper, the long-time dynamical behavior of solutions for the abstract evolution equations with fading memory is investigated on time-dependent spaces. By applying the modified pull-back attractors theory, techniques of a priori estimate and operator decomposition, we verify the asymptotic compactness of the process. Furthermore, the existence and regularity of time-dependent global attractors are proved. This paper improves some known results.
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Key words:
- abstract evolution equation /
- time-dependent attractor /
- fading memory /
- existence /
- regularity
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