The 2D Dirichlet problem for the propagative Helmholtz equation in an exterior domain with cracks and singularities at the edges
type: Item
instance of: scholarly article
title: The 2D Dirichlet problem for the propagative Helmholtz equation in an exterior domain with cracks and singularities at the edges
zbMATH Open document ID: 1251.35023
DOI: 10.1155/2012/340310
author: P. A. Krutitskii
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2012-10-16T00:00:00Z
review text: Summary: The Dirichlet problem for the 2D Helmholtz equation in an exterior domain with cracks is studied. The compatibility conditions at the tips of the cracks are assumed. The existence of a unique classical solution is proved by potential theory. The integral representation for a solution in the form of potentials is obtained. The problem is reduced to the Fredholm equation of the second kind and of index zero, which is uniquely solvable. The asymptotic formulae describing singularities of a solution gradient at the edges (endpoints) of the cracks are presented. The weak solution to the problem may not exist, since the problem is studied under such conditions that do not ensure existence of a weak solution.
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35D30
zbMATH DE Number: 6093810
Wikidata QID: Q58705746
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/340310
OpenAlex ID: W2145644079
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DBLP publication ID: journals/ijmmsc/Krutitskii12
description: scientific article; zbMATH DE number 6093810