The large diffusion limit for the heat equation in the exterior of the unit ball with a dynamical boundary condition

Marek Fila; Kazuhiro Ishige; Tatsuki Kawakami; Johannes Lankeit

doi:10.3934/dcds.2020289

Article Contents

2020, Volume 40, Issue 11: 6549-6566. Doi: 10.3934/dcds.2020289

This issue Previous Article Low regularity of solutions to the Rotation-Camassa-Holm type equation with the Coriolis effect Next Article Global dynamics of a general Lotka-Volterra competition-diffusion system in heterogeneous environments

The large diffusion limit for the heat equation in the exterior of the unit ball with a dynamical boundary condition

1.
Department of Applied Mathematics and Statistics, Comenius University, Mlynská dolina, 84248 Bratislava, Slovakia
2.
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
3.
Applied Mathematics and Informatics Course, Faculty of Advanced Science and Technology, Ryukoku University, 1-5 Yokotani, Seta Oe-cho, Otsu, Shiga 520-2194, Japan
4.
Institut für Mathematik, Universität Paderborn, Warburger Str. 100, 33098 Paderborn, Germany

^* Corresponding author: Johannes Lankeit
^* Corresponding author: Johannes Lankeit

Received: March 31, 2020

Revised: April 30, 2020

Published: July 2020

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Abstract

We study the heat equation in the exterior of the unit ball with a linear dynamical boundary condition. Our main aim is to find upper and lower bounds for the rate of convergence to solutions of the Laplace equation with the same dynamical boundary condition as the diffusion coefficient tends to infinity.

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Mathematics Subject Classification: Primary: 35K05, 35B40.

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References

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