Asymptotic analysis of perturbed Robin problems in a planar domain

Pub Date : 2023-09-11 DOI:10.58997/ejde.2023.57

Paolo Musolino, Martin Dutko, Gennady Mishuris

引用次数: 0

Abstract

We consider a perforated domain \(\Omega(\epsilon)\) of \(\mathbb{R}^2\) with a small hole of size \(\epsilon\) and we study the behavior of the solution of a mixed Neumann-Robin problem in \(\Omega(\epsilon)\) as the size \(\epsilon\) of the small hole tends to \(0\). In addition to the geometric degeneracy of the problem, the nonlinear \(\epsilon\)-dependent Robin condition may degenerate into a Neumann condition for \(\epsilon=0\) and the Robin datum may diverge to infinity. Our goal is to analyze the asymptotic behavior of the solutions to the problem as \(\epsilon\) tends to \(0\) and to understand how the boundary condition affects the behavior of the solutions when \(\epsilon\) is close to \(0\). The present paper extends to the planar case the results of [36] dealing with the case of dimension \(n\geq 3\). For more information see https://ejde.math.txstate.edu/Volumes/2023/57/abstr.html

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平面域上扰动Robin问题的渐近分析

我们考虑一个具有尺寸为\(\epsilon\)的小孔的\(\mathbb{R}^2\)的穿孔域\(\Omega(\epsilon)\)，我们研究了\(\Omega(\epsilon)\)中一个混合Neumann-Robin问题的解在小孔尺寸\(\epsilon\)趋向\(0\)时的行为。除了问题的几何简并性外，非线性\(\epsilon\)依赖的Robin条件对于\(\epsilon=0\)可能简并为Neumann条件，Robin基准可能向无穷远处发散。我们的目标是分析当\(\epsilon\)趋于\(0\)时问题解的渐近行为，并理解当\(\epsilon\)接近\(0\)时边界条件如何影响解的行为。本文将[36]处理尺寸为\(n\geq 3\) .＆＃x0D的结果推广到平面情况;欲了解更多信息，请参阅https://ejde.math.txstate.edu/Volumes/2023/57/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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