Explicit Solution of a Dirichlet Problem in Nonconvex Angle

被引：0
作者：
Merzon A. [1 ]
Zhevandrov P. [2 ]
De la Paz Méndez J.E. [3 ]
Rodríguez M.I.R. [4 ]
机构：
[1] Instituto de Física y Matemáticas, UMSNH, Morelia Michoacán
[2] Facultad de Ciencias Físico-Matemáticas, UMSNH, Morelia Michoacán
[3] Escuela Superior de Matemáticas N.2, UAGro, Cd. Altamirano Guerrero
[4] Facultad de Ciencias Básicas y Aplicadas, Universidad Militar Nueva Granada, Bogotá
来源：
Journal of Mathematical Sciences | 2024年 / 283卷 / 1期
关键词：
Helmholtz equation; method of complex characteristics; nonconvex angle; Sommerfeld integral;
D O I：
10.1007/s10958-024-07241-7
中图分类号：
学科分类号：
摘要：
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. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.
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页码：93 / 110
页数：17
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