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<p>The aim of the paper is to study a differential quasi-variational-hemivariational inequality system of parabolic-parabolic type in a framework of an evolution triple of spaces. The system couples a nonlinear evolution inclusion and a parabolic quasi-variational-hemivariational inequality with a history-dependent operator. First, the nonemptiness and relative compactness of the solution set are established based on the semigroup theory, the Bohnenblust-Karlin fixed point principle, and a surjectivity theorem for L-pseudomonotone operators. Then, the existence of the global pullback attractor of the system is proved by using the theory of measure of noncompactness and results from multivalued non-autonomous dynamical systems. Finally, in order to illustrate the application, the theoretical results are employed to a mathematical model of a dynamic frictional contact problem for viscoelastic materials with long memory and thermal effects.</p>

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Existence of Pullback Attractors for a Class of Differential Quasi-Variational-Hemivariational Inequalities

  • 期刊论文

  • 发表日期：

    2026年3月26日

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  • Shengda Zeng,
  • Jinsheng Du,
  • Stanisław Migórski

摘要

The aim of the paper is to study a differential quasi-variational-hemivariational inequality system of parabolic-parabolic type in a framework of an evolution triple of spaces. The system couples a nonlinear evolution inclusion and a parabolic quasi-variational-hemivariational inequality with a history-dependent operator. First, the nonemptiness and relative compactness of the solution set are established based on the semigroup theory, the Bohnenblust-Karlin fixed point principle, and a surjectivity theorem for L-pseudomonotone operators. Then, the existence of the global pullback attractor of the system is proved by using the theory of measure of noncompactness and results from multivalued non-autonomous dynamical systems. Finally, in order to illustrate the application, the theoretical results are employed to a mathematical model of a dynamic frictional contact problem for viscoelastic materials with long memory and thermal effects.