Optimal control of differential quasivariational inequalities with applications in contact mechanics

TL;DR

This paper establishes the continuous dependence and existence of optimal controls for differential quasivariational inequalities, with applications to contact mechanics involving viscoelastic bodies and free boundary problems.

Contribution

It introduces new theoretical results on the stability and optimal control of differential quasivariational inequalities with practical applications in contact mechanics.

Findings

Proved continuous dependence of solutions on data.

Established existence of optimal controls.

Applied results to a viscoelastic contact problem.

Abstract

We consider a differential quasivariational inequality for which we state and prove the continuous dependence of the solution with respect to the data. This convergence result allows us to prove the existence of at least one optimal pair for an associated control problem. Finally, we illustrate our abstract results in the study of a free boundary problem which describes the equilibrium of a viscoelastic body in frictionless contact with a foundation made of a rigid body coveblack by a rigid-elastic layer.