Large-time behavior of small solutions of a two-dimensional semilinear elliptic equation with a dynamical boundary condition

Marek Fila, Kazuhiro Ishige, Tatsuki Kawakami

研究成果: Article査読

6 被引用数 (Scopus)

抄録

We consider the following initial value problem for a two-dimensional semilinear elliptic equation with a dynamical boundary condition: -Δu=up, x∈R2+, t>0, ∂tu+∂νu=0, x∈∂R2 +, t>0, u(x,0)=φ(x1)≥0, x=(x1,0) ∈∂R2+, where u=u(x,t), ∂t:= ∂/∂t, ∂ν:=-∂/∂x2, R 2+:={(x1,x2): x1∈R, x2>0} and p>1. We show that small solutions behave asymptotically like suitable multiples of the Poisson kernel. This is an extension of previous results of the authors of this paper to the two-dimensional case.

本文言語English
ページ(範囲)107-123
ページ数17
ジャーナルAsymptotic Analysis
85
1-2
DOI
出版ステータスPublished - 2013

ASJC Scopus subject areas

  • 数学 (全般)

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