Differential variational–hemivariational inequalities with application to contact mechanics. (June 2023)

• Record Type: Journal Article
• Authors: Migórski, Stanisław; Cai, Dong-ling; Dudek, Sylwia
• Is Part Of: Nonlinear analysis. Volume 71(2023)
• Publication Date: 2023-06
• Subjects: Differential variational–hemivariational inequality -- Evolution equation -- Evolution triple -- Frictional contact -- Signorini unilateral condition; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103816
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper we study a dynamical system which consists of the Cauchy problem for a nonlinear evolution equation of first order coupled with a nonlinear time-dependent variational–hemivariational inequality with constraint in Banach spaces. The evolution equation is considered in the framework of evolution triple of spaces, and the inequality which involves both the convex and nonconvex potentials. We prove existence of solution by the Kakutani–Ky Fan fixed point theorem combined with the Minty formulation and the theory of hemivariational inequalities. We illustrate our findings by examining a nonlinear quasistatic elastic frictional contact problem for which we provide a result on existence of weak solution.