Rate of convergence in the large diffusion limit for the heat equation with a dynamical boundary condition

Article type: Research Article

Authors: Fila, Marek^{a; *} | Ishige, Kazuhiro^b | Kawakami, Tatsuki^c | Lankeit, Johannes^a

Affiliations: [a] Department of Applied Mathematics and Statistics, Comenius University, 84248 Bratislava, Slovakia. E-mails: fila@fmph.uniba.sk, jlankeit@math.upb.de | [b] Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan. E-mail: ishige@ms.u-tokyo.ac.jp | [c] Department of Applied Mathematics and Informatics, Ryukoku University, Seta Otsu 520-2194, Japan. E-mail: kawakami@math.ryukoku.ac.jp

Correspondence: [*] Corresponding author. E-mail: fila@fmph.uniba.sk.

Abstract: We study the heat equation on a half-space or on an exterior domain with a linear dynamical boundary condition. Our main aim is to establish the rate of convergence to solutions of the Laplace equation with the same dynamical boundary condition as the diffusion coefficient tends to infinity.

Keywords: Heat equation, dynamical boundary condition, large diffusion limit

DOI: 10.3233/ASY-181517

Journal: Asymptotic Analysis, vol. 114, no. 1-2, pp. 37-57, 2019