Error bounds for a class of history-dependent variational inequalities controlled by $\mathcal{D}$-gap~functions

Year 2023, Volume: 52 Issue: 6 - Special Issue: Nonlinear Evolution Problems with Applications, 1550 - 1566, 03.11.2023

Boling Chen Vo Minh Tam

https://doi.org/10.15672/hujms.1183739

Cited By: 2

Abstract

In the present paper, we are concerned with investigating error bounds for history-dependent variational inequalities controlled by the difference gap (for brevity, $\mathcal{D}$-gap) functions. First, we recall a class of elliptic variational inequalities involving the history-dependent operators (for brevity, HDVI). Then, we introduce a new concept of gap functions to the HDVI and propose the regularized gap function for the HDVI via the optimality condition for the concerning minimization problem. Consequently, the $\mathcal{D}$-gap function for the HDVI depends on these regularized gap functions is established. Finally, error bounds for the HDVI controlled by the regularized gap function and the $\mathcal{D}$-gap function are derived under suitable conditions.

Keywords

History-dependent operator, Gap function, Error bound, Variational inequality

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