Contemporary Mathematics. Fundamental DirectionsContemporary Mathematics. Fundamental DirectionsСовременная математика. Фундаментальные направления2413-36392949-0618Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)3349610.22363/2413-3639-2022-68-4-653-670ArticlesСтатьиResearch ArticleExplicit solution of a Dirichlet problem in nonconvex angleЯвное решение задачи Дирихле в невыпуклом углеMerzonA.МерзонА.anatolimx@gmail.comZhevandrovP.ЖевандровП.pzhevand@gmail.comDe la Paz MéndezJ. E.Де ла Пас МендесХ. Э.jeligio12@gmail.comRomero RodriguezM. I.Ромеро РодригесМ. И.maria.romeror@unimilitar.edu.coInstituto de Fiısica y Matemáticas, UMSNHInstituto de Fisica y Matemáticas, UMSNHFacultad de Ciencias Fisico-Matemáticas, UMSNHEscuela Superior de Matemáticas N.2, UAGro, CdEscuela Superior de Matemáticas N.2, UAGroFacultad de Ciencias Básicas y Aplicadas, Universidad Militar Nueva Granada15122022684VOL 68, NO4 (2022)ТОМ 68, №4 (2022)65367006022023Copyright ©; 2022, Merzon A., Zhevandrov P., De la Paz Méndez J.E., Romero Rodriguez M.I.Copyright ©; 2022, Мерзон А., Жевандров П., Де ла Пас Мендес Х.Э., Ромеро Родригес М.И.2022Merzon A., Zhevandrov P., De la Paz Méndez J.E., Romero Rodriguez M.I.Мерзон А., Жевандров П., Де ла Пас Мендес Х.Э., Ромеро Родригес М.И.https://creativecommons.org/licenses/by-nc/4.0https://journals.rudn.ru/CMFD/article/view/33496

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.

В этой работе мы даем явное решение краевой задачи Дирихле для уравнения Гельмгольца в невыпуклом угле с периодическими граничными данными. Мы представляем теоремы единственности и существования в соответствующем функциональном классе и даем явную формулу решения в виде интеграла Зоммерфельда. Используется метод комплексных характеристик [14].

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