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arXiv · 2109.01970

Existence of $φ$-attractor and estimate of their attractive velocity for infinite-dimensional dynamical systems

Chunyan Zhao·Chengkui Zhong·Xiangming Zhu
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Abstract

This paper is devoted to the quantitative study of the attractive velocity of generalized attractors for infinite-dimensional dynamical systems. We introduce the notion of~$φ$-attractor whose attractive speed is characterized by a general non-negative decay function~$φ$, and prove that~$φ$-decay with respect to noncompactness measure is a sufficient condition for a dissipitive system to have a~$φ$-attractor. Furthermore, several criteria for~$φ$-decay with respect to noncompactness measure are provided. Finally, as an application, we establish the existence of a generalized exponential attractor and the specific estimate of its attractive velocity for a semilinear wave equation with a critical nonlinearity.

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Chunyan Zhao, Chengkui Zhong, Xiangming Zhu. 2022-05-06. Existence of $φ$-attractor and estimate of their attractive velocity for infinite-dimensional dynamical systems. https://arxiv.org/abs/2109.01970

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