Convergence to the Poisson kernel  for the Laplace equation  with a nonlinear dynamical boundary condition

Marek Fila; Kazuhiro Ishige; Tatsuki Kawakami

doi:10.3934/cpaa.2012.11.1285

Article Contents

2012, Volume 11, Issue 3: 1285-1301. Doi: 10.3934/cpaa.2012.11.1285

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Convergence to the Poisson kernel for the Laplace equation with a nonlinear dynamical boundary condition

1.
Department of Applied Mathematics and Statistics, Comenius University, 842 48 Bratislava
2.
Mathematical Institute, Tohoku University, Aoba, Sendai 980-8578
3.
Department of Applied Mathematics, Hiroshima University, Higashi-Hiroshima 739-8527

Received: October 31, 2010

Revised: January 31, 2011

Published: April 2012

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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:

Mathematics Subject Classification: Primary: 47J35, 35R11; Secondary: 35B40, 35J65.

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