Penalty Method for a Class of Differential Hemivariational Inequalities with Application. (27th July 2021)

• Record Type: Journal Article
• Authors: Faiz, Zakaria; Baiz, Othmane; Benaissa, Hicham; El Moutawakil, Driss
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 10(2021)
• Page Start: 1178
• Page End: 1200
• Publication Date: 2021-07-27
• Subjects: Differential hemivariational inequality -- existence and uniqueness -- penalty method -- Mosco convergence -- frictional contact problem; 35J87 -- 47J20 -- 49J40 -- 74G30 -- 74M10 -- 74M15 -- 46Txx; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1949346
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we consider a penalty method for a class of differential hemivariational inequalities in reflexive Banach spaces, governed by a set of constraints. First, we recall the existence and uniqueness result of the differential hemivariational inequality. Further, we introduce a penalized problem without constraints and we prove that, as a penalty parameter tends to zero, the solution of the original inequality can be approached to the solution of the penalized problem. Finally, we illustrate our results by an example of a contact problem for which our abstract results can be applied.