In this paper we study a new class of abstract evolution first order hemivariational inequalities which involves constraints and history-dependent operators. First, we prove the existence and uniqueness of solution by using a mixed equilibrium formulation with suitable selected bifunctions combined with a fixed-point principle for history-dependent operators. Next, we deduce existence, uniqueness and regularity results for some special subclasses of problems which include a constrained history-dependent variational–hemivariational inequality, an evolution quasi-variational inequality with constraints, and an evolution second order hemivariational inequality with constraints. Then, we provide an application of the results to a dynamic unilateral viscoelastic frictional contact problem and show its unique weak solvability.

中文翻译：

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具有约束的完全依赖历史的演化半变异不等式

在本文中，我们研究了一类新的抽象演化一阶半变分不等式，它涉及约束和历史相关算子。首先，我们通过使用混合平衡制剂与合适的选择bifunctions与历史相关的运营商的固定点的原则相结合证明溶液存在唯一性。接下来，我们推论出一些特殊的问题子类的存在性，唯一性和规则性结果，其中包括受历史约束的变分-半变分不等式，带约束的演化准变分不等式和带约束的演化二阶半变分不等式。然后，我们将结果应用于动态单边粘弹性摩擦接触问题，并显示其独特的弱可溶性。