Finite-dimensionality of attractors for wave equations with degenerate nonlocal damping
Analysis of PDEs
2023-10-30 v2 Dynamical Systems
Abstract
In this paper we study the fractal dimension of global attractors for a class of wave equations with (single-point) degenerate nonlocal damping. Both the equation and its linearization degenerate into linear wave equations at the degenerate point and the usual approaches to bound the dimension of the entirety of attractors do not work directly. Instead, we develop a new process concerning the dimension near the degenerate point individually and show the finite dimensionality of the attractor.
Cite
@article{arxiv.2309.04712,
title = {Finite-dimensionality of attractors for wave equations with degenerate nonlocal damping},
author = {Zhijun Tang and Senlin Yan and Yao Xu and Chengkui Zhong},
journal= {arXiv preprint arXiv:2309.04712},
year = {2023}
}
Comments
33 pages