FINITE-DIMENSIONALITY OF ATTRACTORS FOR WAVE EQUATIONS WITH DEGENERATE NONLOCAL DAMPING

被引：1

作者：

Tang, Zhijun ^{[1
]}

Yan, Senlin ^{[1
]}

Xu, Yao ^{[2
]}

Zhong, Chengkui ^{[1
]}

机构：

[1] Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China

[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2025年 / 45卷 / 01期

关键词：

Wave equations; degenerate nonlocal damping; global attractors; fractal dimension; Strichartz estimates; GLOBAL ATTRACTORS; P-LAPLACIAN; EVOLUTION-EQUATIONS; DYNAMICS; BEHAVIOR;

D O I：

10.3934/dcds.2024091

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 calculate 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.

引用

页码：219 / 247

页数：29

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