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<p>In this paper, we investigate a mathematical model that describes the dynamic Coulomb’s frictional contact between a thermo-electro-viscoelastic body and an electrically and thermally conductive rigid foundation. Our model incorporates the nonlinear constitutive thermo-electro-viscoelastic law with long-term memory. We outline certain contact, electrical and thermal conditions using Clarke subdifferential. The weak formulation of the problem is derived as a system coupling variational–hemivariational inequalities. We establish the existence and uniqueness of a weak solution to the model by leveraging recent advancements in the theory of variational–hemivariational inequalities and employing a fixed point argument.</p>

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Mathematical analysis for a dynamic thermo-electro-viscoelastic contact problem governed by a system of variational–hemivariational inequalities

  • 期刊论文

  • 发表日期：

    2025年11月8日

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

摘要

In this paper, we investigate a mathematical model that describes the dynamic Coulomb’s frictional contact between a thermo-electro-viscoelastic body and an electrically and thermally conductive rigid foundation. Our model incorporates the nonlinear constitutive thermo-electro-viscoelastic law with long-term memory. We outline certain contact, electrical and thermal conditions using Clarke subdifferential. The weak formulation of the problem is derived as a system coupling variational–hemivariational inequalities. We establish the existence and uniqueness of a weak solution to the model by leveraging recent advancements in the theory of variational–hemivariational inequalities and employing a fixed point argument.