Asymptotics of the solution to Robin problem
type: Item
instance of: scholarly article
title: Asymptotics of the solution to Robin problem
zbMATH Open document ID: 1180.35180
published in: Journal of Mathematical Analysis and Applications
publication date: 2008-11-06T00:00:00Z
review text: The authors consider the following problem: \[ Au:=\nabla^2u=f \text{ on }\mathbb{D}',\;u(\infty)=0\quad\frac{\partial u}{\partial\vec N}-\zeta u=0\text{ on }\Gamma,\tag{1} \] where \(\mathbb{D}\subset\mathbb{R}^3\) is a bounded domain with \(C^\infty\)-boundary \(\Gamma\); \(\mathbb{D}'=\mathbb{R}^3 \setminus\mathbb{D}\), \(\vec N\) is an outer unit normal to \(\Gamma\), \(f\in L^2_0(\mathbb{D}')\), \(\zeta\) is a constant, \(\text{Im}\,\zeta\neq 0\), or \(\text{Im}\,\zeta=0\) and then \(\zeta\geq 0\). The authors adress to the following questions: a) Does \(u\) converge in some sense to the solution of the problem (2) as \(|\zeta|\to\infty\)? \[ \nabla^2w=f \text{ in }\mathbb{D}',\;w(\infty)=0\quad w=0\text{ on }\Gamma\tag{2} \] b) At what rate does \(u\) converge to \(w\) as \(|\zeta|\to\infty\)?
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 5362142
zbMATH Keywords: asymptotics
zbMATH Keywords: Robin problem
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: impedance
author: Hans-Dieter Alber
author: A. G. Ramm
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.08.038
OpenAlex ID: W2065889383
cites work: Q3993273
cites work: Q5724171
cites work: Q3746172
cites work: Many-body wave scattering by small bodies and applications
cites work: Wave scattering by many small particles embedded in a medium
cites work: Q3900553
DOI: 10.1016/J.JMAA.2008.08.038
Recommended article: Q4665250
Recommended article: The asymptotic solution of the bisingular Robin problem
Recommended article: Asymptotic solution of the Robin problem with a regularly singular point
Recommended article: On the asymptotics of a Robin eigenvalue problem
Recommended article: Behavior of solutions for a Robin problem
Recommended article: An asymptotic Robin inequality
Recommended article: On the asymptotic behaviour of the eigenvalues of a Robin problem.
Recommended article: Q3403229
Recommended article: Asymptotic estimation for solution of a class of semi-linear Robin problems
Recommended article: Q3373268
description: scientific article; zbMATH DE number 5362142