The heat equation with the dynamic boundary condition as a singular limit of problems degenerating at the boundary

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED

Asymptotic Analysis Pub Date : 2023-11-10 DOI:10.3233/asy-231862

Yoshikazu Giga, Michał Łasica, Piotr Rybka

引用次数: 0

Abstract

We derive the dynamic boundary condition for the heat equation as a limit of boundary layer problems. We study convergence of their weak and strong solutions as the width of the layer tends to zero. We also discuss Γ-convergence of the functionals generating these flows. Our analysis of strong solutions depends on a new version of the Reilly identity.

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将动态边界条件作为边界退化问题的奇异极限的热方程

作为边界层问题的一种极限，导出了热方程的动态边界条件。研究了它们的弱解和强解在层宽趋于零时的收敛性。我们还讨论了生成这些流的函数Γ-convergence。我们对强解的分析依赖于赖利恒等式的一个新版本。

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

Asymptotic Analysis 数学-应用数学

CiteScore

1.90

自引率

7.10%

发文量

审稿时长

6 months

期刊介绍： The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand. Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.