Convergence to the poisson kernel for the laplace equation with a nonlinear dynamical boundary condition

Fila Marek; Kazuhiro Ishige; Tatsuki Kawakami

doi:10.3934/cpaa.2012.11.1285

Convergence to the poisson kernel for the laplace equation with a nonlinear dynamical boundary condition

Fila Marek, Kazuhiro Ishige, Tatsuki Kawakami

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

Abstract

We study the large time behavior of positive solutions for the Laplace equation on the half-space with a nonlinear dynamical boundary condition. We show the convergence to the Poisson kernel in a suitable sense provided initial data are sufficiently small.

Original language	English
Pages (from-to)	1285-1301
Number of pages	17
Journal	Communications on Pure and Applied Analysis
Volume	11
Issue number	3
DOIs	https://doi.org/10.3934/cpaa.2012.11.1285
Publication status	Published - 2012 May

Keywords

Dynamical boundary conditions
Laplace equation
Poisson kernel

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.3934/cpaa.2012.11.1285

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title = "Convergence to the poisson kernel for the laplace equation with a nonlinear dynamical boundary condition",

abstract = "We study the large time behavior of positive solutions for the Laplace equation on the half-space with a nonlinear dynamical boundary condition. We show the convergence to the Poisson kernel in a suitable sense provided initial data are sufficiently small.",

keywords = "Dynamical boundary conditions, Laplace equation, Poisson kernel",

author = "Fila Marek and Kazuhiro Ishige and Tatsuki Kawakami",

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AU - Ishige, Kazuhiro

AU - Kawakami, Tatsuki

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N2 - We study the large time behavior of positive solutions for the Laplace equation on the half-space with a nonlinear dynamical boundary condition. We show the convergence to the Poisson kernel in a suitable sense provided initial data are sufficiently small.

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Convergence to the poisson kernel for the laplace equation with a nonlinear dynamical boundary condition

Abstract

Keywords

ASJC Scopus subject areas

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