Abstract

In this paper, we consider a penalty method for a class of differential hemivariational inequalities in reflexive Banach spaces, governed by a set of constraints. First, we recall the existence and uniqueness result of the differential hemivariational inequality. Further, we introduce a penalized problem without constraints and we prove that, as a penalty parameter tends to zero, the solution of the original inequality can be approached to the solution of the penalized problem. Finally, we illustrate our results by an example of a contact problem for which our abstract results can be applied.

中文翻译：

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一类具有应用的微分半变分不等式的惩罚方法

摘要

在本文中，我们考虑了自反 Banach 空间中一类微分半变分不等式的惩罚方法，由一组约束控制。首先，我们回顾一下微分半变分不等式的存在唯一性结果。此外，我们引入了一个没有约束的惩罚问题，并证明了当惩罚参数趋于零时，原始不等式的解可以逼近惩罚问题的解。最后，我们通过一个接触问题的例子来说明我们的结果，我们的抽象结果可以应用于这个问题。