Abstract
We consider a mathematical model which describes the equilibrium of an elastic body in contact with two obstacles. We derive its weak formulation which is in a form of an elliptic quasi-variational inequality for the displacement field. Then, under a smallness assumption, we establish the existence of a unique weak solution to the problem. We also study the dependence of the solution with respect to the data and prove a convergence result. Finally, we consider an optimization problem associated with the contact model for which we prove the existence of a minimizer and a convergence result, as well.
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Couderc, M., Sofonea, M. An Elastic Frictional Contact Problem with Unilateral Constraint. Mediterr. J. Math. 15, 195 (2018). https://doi.org/10.1007/s00009-018-1243-4
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DOI: https://doi.org/10.1007/s00009-018-1243-4