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Carleman estimate for a 1D linear elastic problem involving interfaces: Application to an inverse problem
Mathematical Methods in the Applied Sciences ( IF 2.9 ) Pub Date : 2021-04-16 , DOI: 10.1002/mma.7438
Bochra Méjri 1
Affiliation  

The aim of this work is to study the stability of the reconstruction of some mechanical parameters that characterize interfaces within linear elastic bodies. The model considered consists of two bonded elastic solids. The adhesive elastic layer between them is a thin interphase that is approximated, by asymptotic analysis, as an interface. The resulting interface model is in turn characterized by a typical spring-type linear elastic behavior. In this context and on a 1D configuration, we investigate a Carleman-type estimate that relates to a unique continuation principle. The proof is based on the construction of suitable weight functions: their gradients are non-zero, the jumps of the derivatives are positive across the interface, and the averages of the derivatives vanish. The design of such weight functions enables the control of the interface terms in the estimates. With this at hand, we establish a Lipschitz stability estimate for the inverse problem of identifying an interface stiffness parameter from measurements that are available on both sides of the external boundary.

中文翻译:

涉及界面的一维线弹性问题的卡尔曼估计:在逆问题中的应用

这项工作的目的是研究表征线弹性体内界面的一些机械参数的重建的稳定性。所考虑的模型由两个粘合的弹性实体组成。它们之间的粘性弹性层是一个薄的界面,通过渐近分析近似为界面。由此产生的界面模型又以典型的弹簧型线性弹性行为为特征。在这种情况下,在 1D 配置上,我们研究了与独特的延续原理相关的卡尔曼型估计。证明基于合适的权重函数的构造:它们的梯度不为零,导数在界面上的跳跃为正,导数的平均值为零。这种权重函数的设计能够控制估计中的接口项。有了这个,我们建立了一个 Lipschitz 稳定性估计,用于从外部边界两侧可用的测量中识别界面刚度参数的逆问题。
更新日期:2021-04-16
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