The large diffusion limit for the heat equation with a dynamical boundary condition-Reference-Cited by-同舟云学术

The large diffusion limit for the heat equation with a dynamical boundary condition

Published:2020-02-25 Issue:01 Volume:23 Page:2050003
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

Fila Marek¹,Ishige Kazuhiro²,Kawakami Tatsuki³

Affiliation:

1. Department of Applied Mathematics and Statistics, Comenius University, Mlynská dolina, Bratislava 84248, Slovakia

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

3. Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Otsu 520-2194, Japan

Abstract

We study the heat equation on a half-space with a linear dynamical boundary condition. Our main aim is to show that, if the diffusion coefficient tends to infinity, then the solutions converge (in a suitable sense) to solutions of the Laplace equation with the same dynamical boundary condition.

Funder

the Slovak Research and Development Agency

VEGA

the Grant-in-Aid for Scientific Research

the Grant-in-Aid for Young Scientists

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199720500030

Reference38 articles.

1. Asymptotic analysis for the eikonal equation with the dynamical boundary conditions

2. Parabolic problems with dynamical boundary conditions: eigenvalue expansions and blow up

3. Blow Up for Reaction Diffusion Equations Under Dynamical Boundary Conditions†

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