Rad HAZU, Matematičke znanosti, Vol. 29 (2025), 243-259.

OPTIMAL CONTROL OF A FRICTIONAL CONTACT PROBLEM FOR LOCKING MATERIALS

Rachid Guettaf and Arezki Touzaline

Abstract.   In this paper, we consider a bilateral contact with Tresca's friction law between a locking material and a rigid foundation. The goal is to study an optimal control problem which consists of leading the stress tensor as close as possible to a given target, by acting with a control on the boundary of the body. We state an optimal control problem that admits at least one solution. We also introduce the penalized and regularized optimal control problem for which we study the convergence when the penalization and regularization parameter tends to zero.

2020 Mathematics Subject Classification.   49J20, 49J40, 74M10, 74M15.

Key words and phrases.   Optimal control, variational inequalities, locking materials, Tresca's friction law.

DOI: https://doi.org/10.21857/m16wjcwzw9

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