Exponential decay for elastic systems with structural damping and infinite delay. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Luong, Vu Trong; Tung, Nguyen Thanh
• Is Part Of: Applicable analysis. Volume 99:Issue 1(2020)
• Page Start: 13
• Page End: 28
• Publication Date: 2020-01-02
• Subjects: Elastic systems -- structural damping -- infinite delay -- exponential decay; 34G20 -- 34K20 -- 35B35 -- 47H08 -- 47H10; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1484907
• Languages: English
• ISSNs: 0003-6811

Abstract

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.