Periodic unfolding method for domains with very small inclusions

IF 0.8 4区数学 Q2 MATHEMATICS

Electronic Journal of Differential Equations Pub Date : 2023-12-20 DOI:10.58997/ejde.2023.85

J. Avila, Bituin C. Cabarrubias

引用次数: 0

Abstract

This work creates a version of the periodic unfolding method suitable for domains with very small inclusions in \(\mathbb{R}^N\) for \(N\geq 3\). In the first part, we explore the properties of the associated operators. The second part involves the application of the method in obtaining the asymptotic behavior of a stationary heat dissipation problem depending on the parameter \( \gamma < 0\). In particular, we consider the cases when \(\gamma \in (-1,0)\), \( \gamma < -1\) and \(\gamma = -1\). We also include here the corresponding corrector results for the solution of the problem, to complete the homogenization process. For more information see https://ejde.math.txstate.edu/Volumes/2023/85/abstr.html

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极小夹杂物域的周期展开法

这项工作为 \(N\geq 3\) 的 \(\mathbb{R}^N\) 中具有非常小夹杂的域创建了一个周期性展开方法的版本。在第一部分，我们探讨了相关算子的性质。第二部分是应用该方法获得静态散热问题的渐近行为，这取决于参数 \( \gamma < 0\) 。特别是，我们考虑了（gamma在（-1，0））、（gamma <-1）和（gamma =-1）的情况。我们在这里还包含了问题求解的相应校正器结果，以完成同质化过程。更多信息请参见 https://ejde.math.txstate.edu/Volumes/2023/85/abstr.html

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

Electronic Journal of Differential Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.50

自引率

14.30%

发文量

审稿时长

3 months

期刊介绍： All topics on differential equations and their applications (ODEs, PDEs, integral equations, delay equations, functional differential equations, etc.) will be considered for publication in Electronic Journal of Differential Equations.