Analysis and control of stationary inclusions in contact mechanics

We start with a mathematical model which describes the frictionless contact of an elastic body obstacle and prove that it leads to stationary inclusion for strain field. Then, inspired by this model, we consider general in real Hilbert space, governed three parameters. unique solvability as well continuous dependence its solution respect use these results study associated optimal control problem existence convergence results. The proofs are based on arguments monotonicity, compactness, convex analysis lower semicontinuity. apply abstract provide corresponding mechanical interpretations.