论文标题
对于动态粘弹性内聚界面模型的解决方案的存在，能量身份和更高的时间规律性
Existence, energy identity and higher time regularity of solutions to a dynamic visco-elastic cohesive interface model
论文作者
论文摘要
我们研究了通过常见的内聚界面（或等效地，在反平面设置中散开的两个单个域）结合的粘弹性材料的动力学。我们考虑一类一类牵引分离定律，具有正常应力，软化和弹性卸载的激活阈值。以强烈的形式，通过传输和Karush-kuhn-tucker条件（在界面上）的PDES耦合动量平衡系统描述了进化。我们提供对系统的详细分析。我们首先证明存在弱解决方案，采用时间离散方法和初始数据的正则化。然后，我们证明了我们的主要结果：在$ l^\ infty（0，t; l^2）$中加速的能量身份和{solutions}的存在。
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 $L^\infty (0,T; L^2)$.
