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arXiv · 2309.04599

A new class of history-dependent quasi variational-hemivariational inequalities with constraints

S. Migorski·YR. Bai·SD. Zeng
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Abstract

In this paper we consider an abstract class of time-dependent quasi variational-hemivariational inequalities which involves history-dependent operators and a set of unilateral constraints. First, we establish the existence and uniqueness of solution by using a recent result for elliptic variational-hemivariational inequalities in reflexive Banach spaces combined with a fixed-point principle for history-dependent operators. Then, we apply the abstract result to show the unique weak solvability to a quasistatic viscoelastic frictional contact problem. The contact law involves a unilateral Signorini-type condition for the normal velocity and the nonmonotone normal damped response condition while the friction condition is a version of the Coulomb law of dry friction in which the friction bound depends on the accumulated slip.

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S. Migorski, YR. Bai, SD. Zeng. 2023-09-08. A new class of history-dependent quasi variational-hemivariational inequalities with constraints. https://doi.org/10.1016/j.cnsns.2022.106686

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