Pullback attractor for a weakly damped wave equation with sup-cubic nonlinearity

Xinyu Mei; Yangmin Xiong; Chunyou Sun

doi:10.3934/dcds.2020270

Article Contents

2021, Volume 41, Issue 2: 569-600. Doi: 10.3934/dcds.2020270

This issue Previous Article Local rigidity of certain solvable group actions on tori Next Article Maximal factors of order

$ d $

of dynamical cubespaces

Pullback attractor for a weakly damped wave equation with sup-cubic nonlinearity

1.
School of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, Guangdong, China, College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, Guangdong, China
2.
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, Gansu, China

Corresponding author: Chunyou Sun, sunchy@lzu.edu.cn
Corresponding author: Chunyou Sun, sunchy@lzu.edu.cn

Received: December 31, 2019

Revised: April 30, 2020

Early access: July 2020

Published: February 2021

This work was partly supported by the NSFC Grants 11471148, 11522109 and 11871169

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Abstract

In this paper, the non-autonomous dynamical behavior of weakly damped wave equation with a sup-cubic nonlinearity is considered in locally uniform spaces. We first prove the global well-posedness of the Shatah-Struwe solutions, then establish the existence of the $ \big(H_{lu}^{1}(\mathbb{R}^{3})\times L_{lu}^{2}(\mathbb{R}^{3}),H_{\rho}^{1}(\mathbb{R}^{3})\times L_{\rho}^{2}(\mathbb{R}^{3})\big) $-pullback attractor for the Shatah-Struwe solutions process of this equation. The results are based on the recent extension of Strichartz estimates for the bounded domains.

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Mathematics Subject Classification: Primary:35B41, 35Q55, 35Q56, 37L40, 76F20.

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