A class of history-dependent systems of evolution inclusions with applications. (June 2021)

• Record Type: Journal Article
• Authors: Migórski, Stanisław
• Is Part Of: Nonlinear analysis. Volume 59(2021)
• Publication Date: 2021-06
• Subjects: Differential variational inequality -- Differential variational–hemivariational inequality -- History-dependent operator -- Evolution triple -- Inclusion -- Frictional contact; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103246
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper is devoted to studying a system of coupled nonlinear first order history-dependent evolution inclusions in the framework of evolution triples of spaces. The multivalued terms are of the Clarke subgradient or of the convex subdifferential form. Using a surjectivity result for multivalued maps and a fixed point argument for a history-dependent operator, we prove that the system has a unique solution. We conclude with two examples of an evolutionary differential variational–hemivariational inequality and of a dynamic frictional contact problem in mechanics, which illustrate the abstract results.