A Study on Damped Elastic Systems in Banach Spaces. (3rd April 2020)

• Record Type: Journal Article
• Authors: Gou, Haide; Li, Yongxiang
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 5(2020)
• Page Start: 542
• Page End: 570
• Publication Date: 2020-04-03
• Subjects: Damped elastic systems -- mild solution -- analytic and exponentially stable -- existence of solutions; 26A33 -- 34K37 -- 34A08 -- 34A37; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1664567
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this article, we concern with the existence of mild solutions for damped elastic systems. The discussion is based on the operator semigroups theory and fixed point theorem. New forms of the corresponding first order evolution equation are introduced, and their well-posed property is proved by means of the operator semigroup theory. Further, we consider analyticity and exponential of the semigroup associated with the elastic system (1.1 ). Finally, two examples are given to illustrate availability of our results.