A dynamic frictional contact problem between a viscoelastic body and a foundation is studied. The contact is modeled with normal damped response and a friction law. The constitutive law with long memory is assumed to be nonlinear. The existence result is proved using nonlinear monotone operators, fixed point argument, and extension procedure. Moreover, the exponential stability of the energy solution is established using the multiplier method.

中文翻译：

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具有正常阻尼响应和长期记忆的动态摩擦接触问题

研究了粘弹性体与基础之间的动摩擦接触问题。使用正常阻尼响应和摩擦定律对接触进行建模。假设具有长记忆的本构律是非线性的。利用非线性单调算子、不动点论证和可拓过程证明了存在性结果。此外，使用乘子法建立了能量解的指数稳定性。