Optimization problems for a thermoelastic frictional contact problem

• Main Authors: Othmane Baiz, Hicham Benaissa, Rachid Bouchantouf, Driss El Moutawakil
• Format: Article
• Language: English
• Published: Vilnius Gediminas Technical University 2021-09-01
• Series: Mathematical Modelling and Analysis
• Subjects: thermo-elastic material; frictional contact; variational coupled system; convergence results; optimization problem
• Online Access: https://journals.vgtu.lt/index.php/MMA/article/view/12803
• ISSN: 1392-6292; 1648-3510

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.