A Class of History-Dependent Systems of Evolution Inclusions with Applications

TL;DR

This paper investigates a class of history-dependent evolution systems with multivalued terms, proving existence and uniqueness of solutions, and demonstrating applications in mechanics such as variational inequalities and contact problems.

Contribution

It introduces a novel framework for coupled nonlinear history-dependent evolution inclusions with multivalued terms, establishing existence and uniqueness results.

Findings

Proved the existence and uniqueness of solutions for the system.

Applied results to variational-hemivariational inequalities.

Illustrated applications in mechanical contact problems.

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.