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Contemporary Mathematics. Fundamental Directions, 2022, Volume 68, Issue 4, Pages 653–670
DOI: https://doi.org/10.22363/2413-3639-2022-68-4-653-670 (Mi cmfd479) 		 
Explicit solution of a Dirichlet problem in nonconvex angle

A. Merzona, P. Zhevandrova, J. E. De la Paz Méndezb, M. I. Romero Rodríguezc

a UMSNH, Morelia Michoacán, México
b Escuela Superior de Matemáticas N.2, UAGro, Cd. Altamirano Guerrero, México
c Facultad de Ciencias Básicas y Aplicadas, Universidad Militar Nueva Granada, Bogotá Colombia
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DOI: https://doi.org/10.22363/2413-3639-2022-68-4-653-670
Abstract: In the present work, we give an explicit solution of the Dirichlet boundary-value 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 [14] is used.
Keywords: Helmholtz equation, nonconvex angle, Sommerfeld integral, method of complex characteristics.
Funding agency Grant number
CONACYT - Consejo Nacional de Ciencia y Tecnología
Document Type: Article
UDC: 517.956.3+517.958
Language: Russian
Citation: A. Merzon, P. Zhevandrov, J. E. De la Paz Méndez, M. I. Romero Rodríguez, “Explicit solution of a Dirichlet problem in nonconvex angle”, Differential and functional differential equations, CMFD, 68, no. 4, PFUR, M., 2022, 653–670
Citation in format AMSBIB
\Bibitem{MerZheDe 22}
\by A.~Merzon, P.~Zhevandrov, J.~E.~De la Paz M\'endez, M.~I.~Romero Rodr{\'\i}guez
\paper Explicit solution of a Dirichlet problem in nonconvex angle
\inbook Differential and functional differential equations
\serial CMFD
\yr 2022
\vol 68
\issue 4
\pages 653--670
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd479}
\crossref{https://doi.org/10.22363/2413-3639-2022-68-4-653-670}
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