# American Institute of Mathematical Sciences

January  2020, 25(1): 223-240. doi: 10.3934/dcdsb.2019179

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

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

* Corresponding author: Zhijian Yang

Received  December 2018 Revised  March 2019 Published  July 2019

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

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.

Citation: Zhiming Liu, Zhijian Yang. Global attractor of multi-valued operators with applications to a strongly damped nonlinear wave equation without uniqueness. Discrete & Continuous Dynamical Systems - B, 2020, 25 (1) : 223-240. doi: 10.3934/dcdsb.2019179
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