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Optimization problems for a thermoelastic frictional contact problem

    Othmane Baiz   Affiliation
    ; Hicham Benaissa   Affiliation
    ; Rachid Bouchantouf   Affiliation
    ; Driss El Moutawakil   Affiliation

Abstract

In the present paper, we analyze and study the control of a static thermoelastic contact problem. We consider a model which describes a frictional contact problem between a thermoelastic body and a deformable heat conductor obstacle. We derive a variational formulation of the model which is in the form of a coupled system of the quasi-variational inequality of elliptic type for the displacement and the nonlinear variational equation for the temperature. Then, under a smallness assumption, we prove the existence of a unique weak solution to the problem. Moreover, we establish the dependence of the solution with respect to the data and prove a convergence result. Finally, we introduce an optimization problem related to the contact model for which we prove the existence of a minimizer and provide a convergence result.

Keyword : thermo-elastic material, frictional contact, variational coupled system, convergence results, optimization problem

How to Cite
Baiz, O., Benaissa, H., Bouchantouf, R., & El Moutawakil, D. (2021). Optimization problems for a thermoelastic frictional contact problem. Mathematical Modelling and Analysis, 26(3), 444-468. https://doi.org/10.3846/mma.2021.12803
Published in Issue
Sep 9, 2021
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