Analysis and control of a nonlinear boundary value problem

Abstract

We consider a nonlinear two-dimensional boundary value problem which models the frictional contact of a bar with a rigid obstacle. The weak formulation of the problem is in the form of an elliptic variational inequality of the second kind. We establish the existence of a unique weak solution to the problem, then we introduce a regularized version of the variational inequality for which we prove existence, uniqueness and convergence results. We proceed with an optimal control problem for which we prove the existence of an optimal pair. Finally, we consider the corresponding optimal control problem associated to the regularized variational inequality and prove a convergence result.

Boundary optimal control for antiplane contact problems with power-law friction

“…Our results represent a contribution to the optimal control theory of contact problems; see also, e.g., [6,13,14] for other recent results on the existence of optimal controls for problems governed by variational and hemivariational inequalities.…”