A class of history-dependent differential variational inequalities with application to contact problems. (2nd April 2020)

• Record Type: Journal Article
• Authors: Migórski, Stanisław; Liu, Zhenhai; Zeng, Shengda
• Is Part Of: Optimization. Volume 69:Number 4(2020)
• Page Start: 743
• Page End: 775
• Publication Date: 2020-04-02
• Subjects: History-dependent differential variational inequality -- Coulomb law of dry friction -- Signorini condition -- adhesion -- penalty method; 35L15 -- 35L86 -- 35L87 -- 74Hxx -- 74M10; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1647539
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper a class of generalized differential variational inequalities with constraints involving history-dependent operators in Banach spaces is investigated. The unique solvability and regularity results are obtained via surjectivity of multivalued pseudomonotone operators combined with a fixed point principle. From abstract results, a theorem concerning existence, uniqueness and regularity of weak solution to a frictional viscoelastic contact problem with adhesion and history-dependent operator is established. Further, a theoretical analysis of a penalty method for history-dependent differential variational inequality is provided. The unique solvability of a penalized problem is shown, as well as the convergence of its solution to the solution of the original history-dependent differential variational inequality, as a penalty parameter tends to zero. Finally, results on a penalty method are applied to another contact problem, history-dependent frictional viscoelastic contact problem with a generalized normal compliance condition instead of a generalized Signorini contact condition.