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<p>In this paper we consider a general class of coupled systems of time-dependent elliptic quasi-variational-hemivariational inequalities with constraints and history-dependent operators. Each inequality contains a nonlinear operator, a convex potential, a generalized directional derivative of a locally Lipschitz function, a constraint set and history-dependent operators. The existence and uniqueness of the solution of the system is proved based on a result for an elliptic variational inequality combined with the fixed point principle for an almost history-dependent operator. As an application, a unilateral quasi-static frictional contact problem with a thermal effect is studied for which existence, uniqueness and regularity results are provided.</p>

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On Two Coupled History-Dependent Quasi-Variational-Hemivariational Inequalities and Their Applications

  • 期刊论文

  • 发表日期：

    2025年9月25日

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  • Jiangfeng Han,
  • Jiaotong Chen,
  • Stanisław Migórski

摘要

In this paper we consider a general class of coupled systems of time-dependent elliptic quasi-variational-hemivariational inequalities with constraints and history-dependent operators. Each inequality contains a nonlinear operator, a convex potential, a generalized directional derivative of a locally Lipschitz function, a constraint set and history-dependent operators. The existence and uniqueness of the solution of the system is proved based on a result for an elliptic variational inequality combined with the fixed point principle for an almost history-dependent operator. As an application, a unilateral quasi-static frictional contact problem with a thermal effect is studied for which existence, uniqueness and regularity results are provided.