Unique solvability and exponential stability of differential hemivariational inequalities. Issue 14 (25th October 2020)

• Record Type: Journal Article
• Authors: Li, Xiuwen; Liu, Zhenhai; Sofonea, Mircea
• Is Part Of: Applicable analysis. Volume 99:Issue 14(2020)
• Page Start: 2489
• Page End: 2506
• Publication Date: 2020-10-25
• Subjects: Differential hemivariational inequality -- C0-semigroup of operators -- mild solution -- fixed point principle -- exponential stability -- elastic rod -- unilateral contact; 34G20 -- 47J20 -- 49J40 -- 74M15; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1569226
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we study a differential hemivariational inequality (DHVI, for short) in the framework of reflexive Banach spaces. Our aim is three fold. The first one is to investigate the existence and the uniqueness of mild solution, by applying a general fixed-point principle. The second one is to study its exponential stability, by employing the formula for the variation of parameters and inequality techniques. Finally, the third aim is to illustrate an application of our abstract results in the study of an initial and boundary value problem which describes the contact of an elastic rod with an obstacle.