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October  2020, 19(10): 4995-5013. doi: 10.3934/cpaa.2020224

Longtime dynamics for a type of suspension bridge equation with past history and time delay

 1 College of Science, Henan University of Technology, Zhengzhou 450001, China 2 Department of Economic Mathematics, Southwestern University of Finance and Economics, , Chengdu, 611130, China 3 College of Mathematics and Information Science Henan Normal University, Xinxiang 453007, China

* Corresponding author

Received  February 2020 Revised  May 2020 Published  July 2020

Fund Project: Gongwei Liu is partially supported by NSFC (No. 11801145), Key Scientific Research Foundation of the Higher Education Institutions of Henan Province, China (No.19A110004) and the Fund of Young Backbone Teacher in Henan Province (No.2018GGJS068). Baowei Feng is partially supported by NSFC (No. 11701465). Xinguang Yang is partially supported by the Fund of Young Backbone Teacher in Henan Province (No.2018GGJS039)

In this paper, we investigate a suspension bridge equation with past history and time delay effects, defined in a bounded domain $\Omega$ of $\mathbb{R}^N$. Many researchers have considered the well-posedness, energy decay of solution and existence of global attractors for suspension bridge equation without memory or delay. But as far as we know, there are no results on the suspension bridge equation with both memory and time delay. The purpose of this paper is to show the existence of a global attractor which has finite fractal dimension by using the methods developed by Chueshov and Lasiecka. Result on exponential attractors is also proved. We also establish the exponential stability under some conditions. These results are extension and improvement of earlier results.

Citation: Gongwei Liu, Baowei Feng, Xinguang Yang. Longtime dynamics for a type of suspension bridge equation with past history and time delay. Communications on Pure & Applied Analysis, 2020, 19 (10) : 4995-5013. doi: 10.3934/cpaa.2020224
References:

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