Journal of Nonlinear and Variational Analysis

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DOI: 10.23952/jnva.6.2022.5.03

Volume 6, Issue 5, 1 October 2022, Pages 461-481

 

Abstract. This paper is devoted to a generalized time-dependent variational-hemivariational inequality with history-dependent operators. First, we introduce a new concept of gap functions to the time-dependent variational-hemivariational inequality under consideration. Then, we consider a regularized function, which is proved to be a gap function of the inequality problem, and establish several important properties to the regularized function. Furthermore, an global error bound to the time-dependent variational-hemivariational inequality, which implicitly depends on the regularized gap function, is obtained. Finally, a quasi-static contact problem with the constitutive law involving a convex subdifferential inclusion and long memory effect is studied as an illustrative application.

 

How to Cite this Article:
Jinxia Cen, Van Thien Nguyen, Shengda Zeng, Gap functions and global error bounds for history-dependent variational-hemivariational inequalities, J. Nonlinear Var. Anal. 6 (2022), 461-481.