Stability and dynamics of a weak viscoelastic system with memory and nonlinear time-varying delay

Xin-Guang Yang; Jing Zhang; Shu Wang

doi:10.3934/dcds.2020084

Article Contents

2020, Volume 40, Issue 3: 1493-1515. Doi: 10.3934/dcds.2020084

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Stability and dynamics of a weak viscoelastic system with memory and nonlinear time-varying delay

1.
College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
2.
Department of Mathematics and Economics, Virginia State University, Petersburg, VA 23806, USA
3.
College of Applied Science, Beijing University of Technology, Beijing 100124, China

^* Corresponding author: Jing Zhang
^* Corresponding author: Jing Zhang

Received: January 31, 2019

Revised: September 30, 2019

Published: December 2019

Research partly supported by NSFC (No. 11831003, No. 11771031, No. 11531010 and No. 11726625), the Fund of Young Backbone Teacher in Henan Province (No. 2018GGJS039)

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Abstract

This paper is concerned with the stability and dynamics of a weak viscoelastic system with nonlinear time-varying delay. By imposing appropriate assumptions on the memory and sub-linear delay operator, we prove the global well-posedness and stability which generates a gradient system. The gradient system possesses finite fractal dimensional global and exponential attractors with unstable manifold structure. Moreover, the effect and balance between damping and time-varying delay are also presented.

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Mathematics Subject Classification: 35B40, 35B41, 35Q30, 76D03, 76D05.

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