周期域上退化的robin型牵引问题

IF 1.6 3区数学 Q1 MATHEMATICS

Mathematical Modelling and Analysis Pub Date : 2022-09-06 DOI:10.3846/mma.2023.17681

M. D. Riva, Gennady Mishuris, P. Musolino

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引用次数: 0

摘要

我们考虑一种具有周期性空洞的线弹性材料。在空隙边界设置罗宾型牵引条件。然后，我们研究了Robin条件变为纯牵引条件时位移解的渐近性态。也就是说，会有一个矩阵函数b[k](·)，它解析地依赖于一个实参数k，并在k = 0时消失，我们将罗宾条件的狄利克雷部分乘以b[k](·)。我们证明了位移解可以写成k的幂级数，k收敛于0的整个邻域内。对于我们的分析，我们使用泛函分析方法。

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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A Degenerating Robin-Type Traction Problem in a periodic Domain

We consider a linearly elastic material with a periodic set of voids. On the boundaries of the voids we set a Robin-type traction condition. Then, we investigate the asymptotic behavior of the displacement solution as the Robin condition turns into a pure traction one. To wit, there will be a matrix function b[k](·) that depends analytically on a real parameter k and vanishes for k = 0 and we multiply the Dirichlet-like part of the Robin condition by b[k](·). We show that the displacement solution can be written in terms of power series of k that converge for k in a whole neighborhood of 0. For our analysis we use the Functional Analytic Approach.

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