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<p>In our study, we examine a mathematical model that characterizes the dynamic Coulomb’s frictional contact between a thermo-viscoelastic body and a thermally conductive rigid foundation. This model incorporates a nonlinear constitutive viscoelastic law with long-term memory and thermal effects. The contact condition on the contact surface is modeled using Signorini’s boundary condition, expressed through Clarke subdifferential. By formulating the problem’s weak form as a system combining variational–hemivariational inequalities, we establish the existence and uniqueness of a weak solution to the model, leveraging recent advances in the theory of variational–hemivariational inequalities.</p>

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Mathematical Analysis of a Dynamic Signorini’s Contact Problem Governed by a System of Variational–Hemivariational Inequalities in Thermo-Viscoelasticity

  • 期刊论文

  • 发表日期：

    2025年10月28日

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

摘要

In our study, we examine a mathematical model that characterizes the dynamic Coulomb’s frictional contact between a thermo-viscoelastic body and a thermally conductive rigid foundation. This model incorporates a nonlinear constitutive viscoelastic law with long-term memory and thermal effects. The contact condition on the contact surface is modeled using Signorini’s boundary condition, expressed through Clarke subdifferential. By formulating the problem’s weak form as a system combining variational–hemivariational inequalities, we establish the existence and uniqueness of a weak solution to the model, leveraging recent advances in the theory of variational–hemivariational inequalities.