Exponential decay for elastic systems with structural damping and infinite delay

ABSTRACT

In this paper, we consider nonlinear evolution equations of second order in Banach spaces involving unbounded delay, which can model an elastic system with structural damping involving infinite delays. By using fixed point for condensing maps, we prove the existence and exponential decay of mild solutions. The obtained results can be applied to the nonlinear vibration equation of elastic beams with structural damping and infinite delay.

KEYWORDS:

• Elastic systems
• structural damping
• infinite delay
• exponential decay

AMS SUBJECT CLASSIFICATIONS:

• 34G20
• 34K20
• 35B35
• 47H08
• 47H10

Acknowledgements

The authors would like to express their deep appreciation to Prof. Tran Dinh Ke who made great supervisions and contributions to this article completion. They are grateful to the anonymous reviewers for their careful reading, helpful and constructive comments and suggestions, which lead to an improvement of the article.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Vu Trong Luong  http://orcid.org/0000-0002-4640-4348