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

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~$\phi$-attractor whose attractive speed is characterized by a general non-negative decay function~$\phi$, and prove that~$\phi$-decay with respect to noncompactness measure is a sufficient condition for a dissipitive system to have a~$\phi$-attractor. Furthermore, several criteria for~$\phi$-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.

arXiv admin note: substantial text overlap with arXiv:2108.07410

References in corpus (1)

• Asymptotic behaviour of the wave equation with nonlocal weak damping, anti-damping and critical nonlinearity