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<p>In the present paper, we consider a mathematical model describing the dynamic Coulomb’s frictional contact between a thermo-viscoelastic body and a thermally conductive rigid foundation. We employ the nonlinear constitutive viscoelastic law with long-term memory and thermal effects. We describe some contact and thermal conditions with the Clarke subdifferential boundary conditions. We derive the weak formulation of the problem as a system coupling two variational-hemivariational inequalities. We provide results on the existence and uniqueness of a weak solution to the model by using recent results from the theory of variational-hemivariational inequalities. Finally, the continuous dependence of the solution on the data is studied.</p>

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Existence and uniqueness of solutions for a dynamic thermoviscoelastic contact problem governed by an evolutionary variational hemivariational inequality with unilateral constraints

  • 期刊论文

  • 发表日期：

    2025年6月6日

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

摘要

In the present paper, we consider a mathematical model describing the dynamic Coulomb’s frictional contact between a thermo-viscoelastic body and a thermally conductive rigid foundation. We employ the nonlinear constitutive viscoelastic law with long-term memory and thermal effects. We describe some contact and thermal conditions with the Clarke subdifferential boundary conditions. We derive the weak formulation of the problem as a system coupling two variational-hemivariational inequalities. We provide results on the existence and uniqueness of a weak solution to the model by using recent results from the theory of variational-hemivariational inequalities. Finally, the continuous dependence of the solution on the data is studied.