In this paper, we propose a new methodology to study evolutionary variational-hemivariational inequalities based on the theory of evolution equations governed by maximal monotone operators. More precisely, the proposed approach, based on a hidden maximal monotonicity, is used to explore the well-posedness for a class of evolutionary variational-hemivariational inequalities involving history-dependent operators and related problems with periodic and antiperiodic boundary conditions. The applicability of our theoretical results is illustrated through applications to a fractional evolution inclusion and a dynamic semipermeability problem.

中文翻译：

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进化变分-半变分不等式中的隐藏最大单调性

在本文中，我们提出了一种新的方法来研究进化变分-半变分不等式，该方法基于由最大单调算子控制的进化方程理论。更准确地说，所提出的方法，基于隐藏的最大单调性，用于探索一类涉及历史相关算子的进化变分半变分不等式的适定性以及具有周期性和反周期边界条件的相关问题。我们的理论结果的适用性通过对分数演化包含和动态半渗透问题的应用来说明。