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Boundary Optimal Control for a Frictional Contact Problem with Normal Compliance

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Abstract

We consider the contact between an elastic body and a deformable foundation. Firstly, we introduce a mathematical model for this phenomenon by means of a normal compliance contact condition associated with a friction law. Then, we propose a variational formulation of the model in a form of a quasi-variational inequality governed by a non-differentiable functional and we briefly discuss its well-possedness. Nextly, we address an optimal control problem related to this model in order to led the displacement field as close as possible to a given target by acting with a localized boundary control. By using some mollifiers of the normal compliance functions, we introduce a regularized model which allows us to establish an optimality condition. Finally, by means of asymptotic analysis tools, we show that the solutions of the regularized optimal control problems converge to a solution of the initial optimal control problem.

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Acknowledgements

This work was supported by a Grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, Project number PN-II-ID-PCE-2011-3-0257 and by a LEA MATH-MODE Project CNRS-IMAR.

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Authors and Affiliations

  1. Department of Mathematics, University of Craiova, A.I.Cuza 13, 200585, Craiova, Romania

    Andaluzia Matei & Sorin Micu

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  1. Andaluzia Matei
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  2. Sorin Micu
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Correspondence to Andaluzia Matei.

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Matei, A., Micu, S. Boundary Optimal Control for a Frictional Contact Problem with Normal Compliance. Appl Math Optim 78, 379–401 (2018). https://doi.org/10.1007/s00245-017-9410-8

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