Long-time dynamics for a nonlinear Timoshenko system with delay

Abstract

This paper is concerned with a nonlinear Timoshenko system with a time delay term in the internal feedback together with initial data and Dirichet boundary conditions. Under some suitable assumptions on the weights of feedback, we obtain the existence of a global attractor with finite fractal dimension for the case of equal speed wave propagation. Furthermore, the existence of exponential attractors is also derived.

Keywords:

• Timoshenko system
• delay feedback
• global attractor
• finite fractal dimension

AMS Subject Classifications:

• 37L05
• 37L30

Acknowledgements

Xinguang Yang takes his acknowledges to ICMC-USP in Brazil as a post-doctor from May 2015 to May 2016. The authors express sincere thanks to the editors and referees for their constructive comments and suggestions that helped to improve this paper.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11526164]; the Fundamental Research Funds for the Central Universities [grant number JBK160122]; and by FAPESP in Brazil [grant number 2014/17080-0].