The global attractor for the wave equation with nonlocal strong damping

Biyue Chen; Chunxiang Zhao; Chengkui Zhong

doi:10.3934/dcdsb.2021015

Article Contents

2021, Volume 26, Issue 12: 6207-6228. Doi: 10.3934/dcdsb.2021015 open access

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The global attractor for the wave equation with nonlocal strong damping

1.
Department of Mathematics, Nanjing University, Nanjing, 210093, China
2.
Institute of Applied System Analysis, Jiangsu University, Zhenjiang, 212013, China

^* Corresponding author: ckzhong@nju.edu.cn
^* Corresponding author: ckzhong@nju.edu.cn

Received: November 30, 2019

Revised: September 30, 2020

Early access: January 2021

Published: December 2021

The first author is supported by NSFC(11731005)

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Abstract

The paper is devoted to establishing the long-time behavior of solutions for the wave equation with nonlocal strong damping: $ u_{tt}-\Delta u-\|\nabla u_{t}\|^{p}\Delta u_{t}+f(u) = h(x). $ It proves the well-posedness by means of the monotone operator theory and the existence of a global attractor when the growth exponent of the nonlinearity $ f(u) $ is up to the subcritical and critical cases in natural energy space.

Keywords:

Wave equation,
nonlocal strong damping,
global attractor,
subcritical and critical growth exponent.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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References

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