ON THE 1D WAVE EQUATION IN TIME-DEPENDENT DOMAINS AND THE PROBLEM OF DEBOND INITIATION

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ON THE 1D WAVE EQUATION IN TIME-DEPENDENT DOMAINS AND THE PROBLEM OF DEBOND INITIATION

机译：时域上的一维波方程和解键的问题

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Motivated by a debonding model for a thin film peeled from a substrate, we analyse the one-dimensional wave equation, in a time-dependent domain which is degenerate at the initial time. In the first part of the paper we prove existence for the wave equation when the evolution of the domain is given; in the second part of the paper, the evolution of the domain is unknown and is governed by an energy criterion coupled with the wave equation. Our existence result for such coupled problem is a contribution to the study of crack initiation in dynamic fracture.

机译：根据从基材上剥离的薄膜的脱粘模型的激励，我们在与时间相关的域中分析了一维波动方程，该方程在初始时间就退化了。在本文的第一部分中，当给出域的演化时，我们证明了波动方程的存在。在本文的第二部分中，域的演化是未知的，并且受能量准则和波动方程的约束。我们对于这种耦合问题的存在结果为动态断裂中裂纹萌生的研究做出了贡献。

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《ESAIM》 |2019年第1期|80.1-80.21|共21页
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作者单位

Univ Firenze Dipartimento Matemat & Informat U Dini Viale Morgagni 67-A I-50134 Florence Italy;

SISSA Via Bonomea 265 I-34136 Trieste Italy;

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正文语种 eng
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关键词
Wave equation in time-dependent domains; singularities; dynamic debonding; dynamic energy release rate; Griffith's criterion; dynamic fracture; crack initiation; thin films;

机译：时变域中的波动方程;奇点动态脱胶动态能量释放率;格里菲斯准则;动态断裂裂纹萌生薄膜;

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ON THE 1D WAVE EQUATION IN TIME-DEPENDENT DOMAINS AND THE PROBLEM OF DEBOND INITIATION

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