Optimal Control of a Variational Inequality with Application to the Kirchhoff Plate Having Small Flexural Rigidity

Abstract

This paper concerns an optimal control problem of elliptic singular perturbations in variational inequalities (with controls appearing in coefficients, right-hand sides and convex sets of states as well). The existence of an optimal control is verified. The applications to the optimal design of an elastic plate with a small rigidity and with inner (or moving) obstacle a primal finite element model is applied and convergence result is obtained.