动态粘弹粘结界面模型解的存在性、能量恒等式及高阶正则性
Existence, energy identity and higher time regularity of solutions to a dynamic visco-elastic cohesive interface model
摘要：
本文研究了粘弹性材料在反平面情况下由一个共同的粘结界面（或等效地由一个规定的粘结裂纹隔开的两个单畴）耦合的动力学问题。我们考虑了一般类的牵引分离法的激活阈值的正常应力，软化和弹性卸载。在强形式中，演化描述的偏微分方程耦合动量平衡（在散装）与传输和Karush-Kuhn-Tucker条件（在界面上）的系统。我们对该系统进行了详细的分析。我们首先证明存在的弱解，采用时间离散的方法和正则化的初始数据。然后，我们证明了我们的主要结果：能量恒等式和加速度下$L^\infty (0,T; L^2)$的{解}的存在性。
英文摘要：
We study the dynamics of visco-elastic materials coupled by a common cohesive interface (or, equivalently, {two single domains separated by} a prescribed cohesive crack) in the anti-plane setting. We consider a general class of traction-separation laws featuring an activation threshold on the normal stress, softening and elastic unloading. In strong form, the evolution is described by a system of PDEs coupling momentum balance (in the bulk) with transmission and Karush-Kuhn-Tucker conditions (on the interface). We provide a detailed analysis of the system. We first prove existence of a weak solution, employing a time discrete approach and a regularization of the initial data. Then, we prove our main results: the energy identity and the existence of { solutions} with acceleration in $L^\infty (0,T; L^2)$.
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