danДоклады Национальной академии наук БеларусиDoklady of the National Academy of Sciences of Belarus1561-83232524-2431The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-8323-2022-66-3-263-268dan-1062Research ArticleМАТЕМАТИКАMATHEMATICSМетод отражений для уравнения Клейна–ГордонаMethod of reflections for the Klein–Gordon equationКорзюкВ. И.KorzyukV. I.

Корзюк Виктор Иванович – академик, д-р физ.-мат. наук, профессор

ул. Сурганов а, 11, 220072, Минск

Korzyuk Viktor I. – Academician, D. Sc. (Physics and Ma thematics),  Professor

11, Surganov Str., 220072, Minsk

korzyuk@bsu.byhttps://orcid.org/0000-0002-1482-9106РудькоЯ. В.RudzkoJ. V.

Рудько Ян Вячеславович – магистр (математика и компьютерные науки)

пр.  Независимости,  4, 220030,  Минск

Rudzko  Jan  V.  –  M. Sc. (Mathematiсs and Computer Sciences)

4,  Nezavisimosti Ave., 220030,  Minsk

janycz@yahoo.comИнститут математики Национальной академии наук Беларуси; Белорусский государственный университетInstitute of Mathematics of the National Academy of Sciences of Belarus; Belarusian State UniversityБелорусский государственный университетBelarusian State University202230062022663263268Copyright © Корзюк В.И., Рудько Я.В., 20222022Корзюк В.И., Рудько Я.В.Korzyuk V.I., Rudzko J.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://doklady.belnauka.by/jour/article/view/1062

 Методом отражений в явном аналитическом виде выписаны решения первой и второй смешанных задач для однородного уравнения Клейна–Гордона в четверти плоскости и первой смешанной задачи для однородного уравнения Клейна–Гордона в полуполосе с неоднородными условиями Коши и однородным условием Дирихле (или условием Неймана). Сформулированы условия, при которых решения данных задач являются классическими. 

Using the method of reflections, the solutions of the first and second mixed problem for the homogenous Klein–Gordon equation in a quarter plane and of the first mixed problem for the homogenous Klein–Gordon equation in a halfstrip are written out in an explicit analytical form. The Cauchy conditions of these problems are inhomogeneous, but the Dirichlet boundary condition (or the Neumann boundary condition) is homogeneous. Conditions are formulated, under which the solutions to these problems are classical.

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The authors declare that there are no conflicts of interest present.