In this paper we analyse a one-dimensional debonding model when viscosity is taken into account. It is described by the weakly damped wave equation whose domain, the debonded region, grows according to a Griffith’s criterion. Firstly we prove that the equation admits a unique solution when the evolution of the debonding front is assigned. Finally we provide an existence and uniqueness result for the coupled problem given by the wave equation together with Griffith’s criterion.

中文翻译：

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一维带阻尼脱胶模型动力学演化的存在与唯一性

在本文中，我们分析了考虑粘度的一维脱粘模型。它由弱阻尼波动方程描述，该波动方程的域（解粘区域）根据格里菲斯准则增长。首先，我们证明当指定了脱粘前沿的演化时，该方程式有一个唯一的解。最后，我们提供了波动方程与格里菲斯准则一起给出的耦合问题的存在性和唯一性结果。