Explicit solution of a Dirichlet problem in nonconvex angle

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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.

About the authors

A. Merzon

Instituto de Fiısica y Matemáticas, UMSNH

Email: anatolimx@gmail.com
Morelia Michoac´an, M´exico

P. Zhevandrov

Facultad de Ciencias Fisico-Matemáticas, UMSNH

Email: pzhevand@gmail.com
Morelia Michoac´an, M´exico

J. E. De la Paz Méndez

Escuela Superior de Matemáticas N.2, UAGro, Cd

Email: jeligio12@gmail.com
Altamirano Guerrero, M´exico

M. I. Romero Rodriguez

Facultad de Ciencias Básicas y Aplicadas, Universidad Militar Nueva Granada

Author for correspondence.
Email: maria.romeror@unimilitar.edu.co
Bogota´ Colombia

References

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Copyright (c) 2022 Merzon A., Zhevandrov P., De la Paz Méndez J.E., Romero Rodriguez M.I.

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