The heat equation with the dynamic boundary condition as a singular limit of problems degenerating at the boundary-Reference-Cited by-同舟云学术

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

Published:2023-11-10 Issue:3-4 Volume:135 Page:463-508
ISSN:1875-8576
Container-title:Asymptotic Analysis
language:
Short-container-title:ASY

Author:

Giga Yoshikazu¹,Łasica Michał¹²,Rybka Piotr³

Affiliation:

1. Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba Meguro-ku Tokyo 153-8914, Japan

2. Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warszawa, Poland

3. Institute of Applied Mathematics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland

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.

Publisher

IOS Press

Subject

General Mathematics

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