Optimal Control Problems for Evolutionary Variational Inequalities with Volterra type Operators

TL;DR

This paper studies optimal control problems involving evolution inclusions with history-dependent Volterra operators, establishing solution existence under certain conditions, with applications in various engineering and physical processes.

Contribution

It introduces a framework for optimal control of evolution inclusions with Volterra operators, extending previous models to account for history-dependent dynamics.

Findings

Existence of solutions under specified hypotheses

Application to injection molding and contact mechanics

Framework applicable to electro-wetting problems

Abstract

In this paper, we consider the optimal control problem for a class of evolution inclusions with Volterra type operators, which can be history-dependent. We establish the existence of a solution to the stated optimal control problem under some hypothesis on data-in. The motivation for this work comes from the optimal control problems for variational inequalities arising in the study of injection molding processes, contact mechanics, principles of electro-wetting on dielectric, and others.