Open AccessOPTIMIZATION PROBLEMS FOR A THERMOELASTIC FRICTIONAL CONTACT PROBLEM
Author(s) -
Othmane Baiz,
Hicham Benaissa,
Rachid Bouchantouf,
Driss El Moutawakil
Publication year - 2021
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/mma.2021.12803
Subject(s) - thermoelastic damping , variational inequality , mathematics , unilateral contact , convergence (economics) , displacement (psychology) , nonlinear system , mathematical analysis , physics , thermal , finite element method , psychology , quantum mechanics , meteorology , psychotherapist , thermodynamics , economic growth , economics
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.