This work considers a mathematical model describing a dynamic frictional contact between a viscoelastic body and an adhesive foundation. The contact is modeled with normal damped response condition associated with a new version of Coulomb’s law of dry friction with adhesion introducing a new term which gives a better transition from adhesion to friction. We present a variational formulation of the problem which is given as a system coupling an evolution inequality of the second order for the displacement and a differential equation of the first order for the bonding field. We establish the existence and uniqueness of the weak solution. The proof is based on parabolic variational inequalities of the second kind, differential equations and fixed point theorem.

这项工作考虑了一个数学模型，该模型描述了粘弹性体和粘合剂基础之间的动态摩擦接触。接触是在正常阻尼响应条件下建模的，该条件与新版库仑定律的干摩擦定律相关联，而粘着力引入了一个新术语，该术语可以更好地实现从粘着到摩擦的过渡。我们提出了该问题的变分形式，该变分形式是一个系统，该系统耦合了位移的二阶演化不等式和键合场的一阶微分方程。我们确定了弱解的存在性和唯一性。该证明基于第二类抛物线变分不等式，微分方程和不动点定理。