2021/09/05 by Zhao, Chunyan, Zhong, Chengkui, Zhu, Xiangming
#35B40 #35B41 #35L05 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2109.01970
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.