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The 2D Dirichlet Problem for the Propagative Helmholtz Equation in an Exterior Domain with Cracks and Singularities at the Edges
Author
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-07-01
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Krutitskii, P. A.. 2012. The 2D Dirichlet Problem for the Propagative Helmholtz Equation in an Exterior Domain with Cracks and Singularities at the Edges. International Journal of Mathematics and Mathematical Sciences،Vol. 2012, no. 2012, pp.1-18.
https://search.emarefa.net/detail/BIM-464111
Modern Language Association (MLA)
Krutitskii, P. A.. The 2D Dirichlet Problem for the Propagative Helmholtz Equation in an Exterior Domain with Cracks and Singularities at the Edges. International Journal of Mathematics and Mathematical Sciences No. 2012 (2012), pp.1-18.
https://search.emarefa.net/detail/BIM-464111
American Medical Association (AMA)
Krutitskii, P. A.. The 2D Dirichlet Problem for the Propagative Helmholtz Equation in an Exterior Domain with Cracks and Singularities at the Edges. International Journal of Mathematics and Mathematical Sciences. 2012. Vol. 2012, no. 2012, pp.1-18.
https://search.emarefa.net/detail/BIM-464111
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-464111