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<p>We propose three modified contact boundary conditions incorporating both the velocity and the displacement with a parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\delta \)</EquationSource> </InlineEquation> for the viscoelastic problem. As <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\delta \)</EquationSource> </InlineEquation> approaches 0, these conditions formally reduce to the conventional Signorini, Tresca-friction, and Clarke-subdifferential type boundary conditions, respectively. Consequently, the modified conditions, as a generalization of the conventional ones, can be viewed as contact conditions in the displacement with a dynamic setting. We derive weak formulations for the viscoelastic contact model under three modified contact conditions and explore their well-posedness. Additionally, we provide bounds on the weak solutions with respect to the parameter <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\delta \)</EquationSource> </InlineEquation>.</p>

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Well-posedness of viscoelastic contact problems with modified Signorini, Tresca-friction, and Clarke-subdifferential type contact conditions incorporating both velocity and displacement

  • 期刊论文

  • 发表日期：

    2025年11月21日

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  • Chang Wang,
  • Yi-Bin Xiao,
  • Guanyu Zhou,
  • Weimin Han,
  • Yichen Ren

摘要

We propose three modified contact boundary conditions incorporating both the velocity and the displacement with a parameter \(\delta \) for the viscoelastic problem. As \(\delta \) approaches 0, these conditions formally reduce to the conventional Signorini, Tresca-friction, and Clarke-subdifferential type boundary conditions, respectively. Consequently, the modified conditions, as a generalization of the conventional ones, can be viewed as contact conditions in the displacement with a dynamic setting. We derive weak formulations for the viscoelastic contact model under three modified contact conditions and explore their well-posedness. Additionally, we provide bounds on the weak solutions with respect to the parameter \(\delta \) .