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<p>In this paper, we propose and study a new differential variational-hemivariational inequality system obtained by mixing a nonlinear evolutionary equation, a variational -hemivariational inequality and a parabolic variational inequality in Banach spaces. By applying the surjectivity theorem, the semigroup theory, and the fixed point theorem, we prove the unique solvability of this system. Moreover, as an application, we apply our theoretical results to analyze a frictionless viscoelastic contact problem with long-memory effects, wear, and damage.</p>

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A New Differential Variational-Hemivariational Inequality System and Its Applications

  • 期刊论文

  • 发表日期：

    2026年1月29日

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  • Wei Li,
  • Yu Wang,
  • Zengbao Wu,
  • Zhenghui Tang,
  • Qixia Zhang

摘要

In this paper, we propose and study a new differential variational-hemivariational inequality system obtained by mixing a nonlinear evolutionary equation, a variational -hemivariational inequality and a parabolic variational inequality in Banach spaces. By applying the surjectivity theorem, the semigroup theory, and the fixed point theorem, we prove the unique solvability of this system. Moreover, as an application, we apply our theoretical results to analyze a frictionless viscoelastic contact problem with long-memory effects, wear, and damage.