Fully history-dependent quasivariational inequalities in contact mechanics. Issue 11 (1st November 2016)

• Record Type: Journal Article
• Authors: Sofonea, Mircea; Xiao, Yi-bin
• Is Part Of: Applicable analysis. Volume 95:Issue 11(2016)
• Page Start: 2464
• Page End: 2484
• Publication Date: 2016-11-01
• Subjects: Fully history-dependent quasivariational inequalities -- existence and uniqueness -- fixed-point theorem -- quasistatic frictional contact -- viscoelastic materials; 49J40 -- 74M10 -- 74M15 -- 74H20 -- 74H25; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2015.1093623
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper, we consider a new class of fully history-dependent quasivariational inequalities which arise in the study of quasistatic models of contact and involve two history-dependent operators. By using a fixed-point theorem and arguments of monotonicity and convexity, we prove an existence and uniqueness result of the solution, which includes as special cases some results already obtained in some papers. Then, the obtained result is applied to two problems of quasistatic frictional contact for viscoelastic materials and the unique weak solvability of each contact problem is obtained.