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Optimal control of a contact problem with slip dependent friction

Abstract The aim of this paper is to study a frictional contact problem between an elastic body and a foundation. We focus on the optimal control of the model which consists of acting with a control on a portion of the boundary of the body and leading the stress tensor as close as possible to a given target. We state an optimal control problem for which we establish an existence theorem of the solution. We then introduce a sequence of regularized problems depending on a positive parameter α and we study the convergence of the sequence of the solutions when the parameter α tends to zero. Finally, an optimality condition is established for this problem.