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<p>In this paper, we address control problems for a mathematical model describing the dynamic Coulomb frictional contact between a thermo-electro-viscoelastic body and a rigid foundation that is electrically and thermally conductive. The contact, friction, electrical, and thermal conductivity conditions on the contact surface are formulated using the Clarke subdifferential. We derive the weak formulation of the problem as a system coupling a variational–hemivariational inequality with two hemivariational inequalities. We establish results on the existence and uniqueness of a weak solution to the model and, under additional assumptions, demonstrate the continuous dependence of the solution on the problem’s data. Finally, for a class of optimal control problems, we prove the existence of optimal solutions.</p>

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Optimal control for a dynamic contact problem governed by a system of hemivariational inequalities in thermo-electro-viscoelasticity

  • 期刊论文

  • 发表日期：

    2025年1月14日

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  • Alaoui Mohammed,
  • Bouallala Mustapha,
  • Essoufi El Hassan,
  • Ouaanabi Abdelhafid

摘要

In this paper, we address control problems for a mathematical model describing the dynamic Coulomb frictional contact between a thermo-electro-viscoelastic body and a rigid foundation that is electrically and thermally conductive. The contact, friction, electrical, and thermal conductivity conditions on the contact surface are formulated using the Clarke subdifferential. We derive the weak formulation of the problem as a system coupling a variational–hemivariational inequality with two hemivariational inequalities. We establish results on the existence and uniqueness of a weak solution to the model and, under additional assumptions, demonstrate the continuous dependence of the solution on the problem’s data. Finally, for a class of optimal control problems, we prove the existence of optimal solutions.