On the wave equation on moving domains: regularity, energy balance and application to dynamic debonding

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-03-07 DOI:10.4171/ifb/485

G. Lazzaroni, Riccardo Molinarolo, F. Riva, Francesco Solombrino

引用次数: 0

Abstract

. We revisit some issues about existence and regularity for the wave equation in noncylindrical domains. Using a method of diﬀeomorphisms, we show how, through increasing regularity assumptions, the existence of weak solutions, their improved regularity and an energy balance can be derived. As an application, we give a rigorous deﬁnition of dynamic energy release rate density for some problems of debonding, and we formulate a proper notion of solution for such problems. We discuss the consistence of such formulation with previous ones, given in literature for particular cases.

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运动域上的波动方程:规律、能量平衡及其在动态脱粘中的应用

．我们重新讨论了非柱域波动方程的存在性和规律性问题。利用微分同态的方法，我们证明了如何通过增加正则性假设，推导出弱解的存在性、改进的正则性和能量平衡。作为应用，我们给出了一些脱粘问题的动态能量释放率密度的严格定义，并对这类问题给出了适当的解的概念。我们讨论这种公式的一致性与先前的，在文献中给出的特殊情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.