Global attractor of multi-valued operators with applications to a strongly damped nonlinear wave equation without uniqueness

Zhiming Liu; Zhijian Yang

doi:10.3934/dcdsb.2019179

Article Contents

2020, Volume 25, Issue 1: 223-240. Doi: 10.3934/dcdsb.2019179

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Global attractor of multi-valued operators with applications to a strongly damped nonlinear wave equation without uniqueness

Zhiming Liu and
Zhijian Yang^,

School of Mathematics and Statistics, Zhengzhou University, No.100, Science Road, Zhengzhou 450001, China

^* Corresponding author: Zhijian Yang
^* Corresponding author: Zhijian Yang

Received: December 2018

Revised: March 2019

Early access: July 2019

Published: January 2020

This work is supported by NSFC (Grant No. 11671367)

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Abstract

The paper investigates the existence of global attractors for a few classes of multi-valued operators. We establish some criteria and give their applications to a strongly damped wave equation with fully supercritical nonlinearities and without the uniqueness of solutions. Moreover, the geometrical structure of the global attractors of the corresponding multi-valued operators is shown.

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Mathematics Subject Classification: Primary: 37L05, 37L30; Secondary: 35B33, 35B40, 35B41.

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