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Optimal control of a bilateral contact with friction

Volume 49 / 2022

Arezki Touzaline Applicationes Mathematicae 49 (2022), 21-34 MSC: 49J40, 74B20, 74M10, 74M15. DOI: 10.4064/am2405-4-2021 Published online: 30 August 2021


We consider a mathematical model which describes a static frictional contact between a nonlinear elastic body and a rigid foundation. The contact is modelled with Tresca’s nonlocal friction law. We derive a variational formulation and prove its unique weak solvability under a certain condition on the friction coefficient. We state an optimal control problem which consists in leading the stress tensor as close as possible to a given target, by acting with a control on the boundary of the body. We prove that the optimal control admits a solution, and then we study a regularized control problem and establish a convergence result.


  • Arezki TouzalineFaculté de Mathématiques, USTHB
    Laboratoire des Systèmes Dynamiques
    BP 32 El Alia, Bab-Ezzouar
    16111 Alger, Algeria

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