The aim of the paper is to introduce and investigate a dynamical system which consists of a variational–hemivariational inequality of hyperbolic type combined with a non-linear evolution equation. Such a dynamical system arises in studies of complicated contact problems in mechanics. Existence, uniqueness and regularity of a global solution to the system are established. The approach is based on a new semi-discrete approximation with an application of a surjectivity result for a pseudomonotone perturbation of a maximal monotone operator. A new dynamic viscoelastic frictional contact model with adhesion is studied as an application, in which the contact boundary condition is described by a generalised normal damped response condition with unilateral constraint and a multivalued frictional contact law.

中文翻译：

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由非线性演化方程驱动的一类新的双曲变分-半变分不等式

本文的目的是介绍和研究一个由双曲型变分-半变分不等式和非线性演化方程组成的动力系统。这样的动力系统出现在力学中复杂的接触问题的研究中。建立了系统全局解的存在性、唯一性和规律性。该方法基于一种新的半离散近似，其中应用了一个最大单调算子的伪单调扰动的满射性结果。研究了一种新的具有粘附性的动态粘弹性摩擦接触模型，其中接触边界条件由具有单边约束的广义法向阻尼响应条件和多值摩擦接触定律描述。