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

IF 1.2 4区数学 Q1 MATHEMATICS

Interfaces and Free Boundaries Pub Date : 2022-03-07 DOI:10.4171/ifb/485

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

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引用次数: 0

摘要

．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。

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

. 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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来源期刊

Interfaces and Free Boundaries 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Interfaces and Free Boundaries is dedicated to the mathematical modelling, analysis and computation of interfaces and free boundary problems in all areas where such phenomena are pertinent. The journal aims to be a forum where mathematical analysis, partial differential equations, modelling, scientific computing and the various applications which involve mathematical modelling meet. Submissions should, ideally, emphasize the combination of theory and application.