Existence theorem for the solution of Dirichlet and Neumann problems for the Helmholtz equation in the quasiperiodic case
type: Item
instance of: scholarly article
title: Existence theorem for the solution of Dirichlet and Neumann problems for the Helmholtz equation in the quasiperiodic case
zbMATH Open document ID: 0683.35020
DOI: 10.1007/BF00969727
published in: Siberian Mathematical Journal
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/62950
review text: Consider the Dirichlet and the Neumann quasiperiodic problems for the Helmholtz equation \[ (1)\quad (\Delta +k^ 2)u=0,\quad k>0,\quad (x,y)\in \Omega \subset R^ 2 \] in two different cases of \(\Omega\). The so called quasiperiodicity means that \[ u(x+2\pi,y)=u(x,y)\exp (2\pi i\alpha)\quad \forall (x,y)\in \Omega \] where \(\alpha\) is a fixed real number. The author gives existence theorems for solutions of these problems.
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 4118785
zbMATH Keywords: Dirichlet and Neumann problem
zbMATH Keywords: existence theorem
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: quasiperiodicity
author: Vasilii M. Babich
MaRDI profile type: Publication
cites work: Scattering theory for the d'Alembert equation in exterior domains
cites work: Q3701866
description: scientific article; zbMATH DE number 4118785