Explicit Solution of a Dirichlet Problem in Nonconvex Angle

In the present work, we give an explicit solution of the Dirichlet boundary problem for the Helmholtz equation in a nonconvex angle with periodic boundary data. We present uniqueness and existence theorems in an appropriate functional class and we give an explicit formula for the solution in the for...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2024, Vol.283 (1), p.93-110
Main Authors: Merzon, A., Zhevandrov, P., De la Paz Méndez, J. E., Rodríguez, M. I. Romero
Format: Article
Language:English
Subjects:
Dirichlet problem
Existence theorems
Helmholtz equations
Mathematics
Mathematics and Statistics
Uniqueness theorems
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Summary:In the present work, we give an explicit solution of the Dirichlet boundary problem for the Helmholtz equation in a nonconvex angle with periodic boundary data. We present uniqueness and existence theorems in an appropriate functional class and we give an explicit formula for the solution in the form of the Sommerfeld integral. The method of complex characteristics [12] is used.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-024-07241-7