vestifmИзвестия Национальной академии наук Беларуси. Серия физико-математических наукProceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series1561-24302524-2415The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-2430-2025-61-3-183-194vestifm-848Research ArticleМАТЕМАТИКАMATHEMATICSСмешанная задача для волнового уравнения в криволинейной полуполосе с разрывными начальными даннымиA mixed problem for the wave equation in a curvilinear halfstrip with discontinuous initial dataКорзюкВ. И.KorzyukV. I.

Виктор Иванович Корзюк – академик Национальной академии наук Беларуси, доктор физико-математических наук, профессор

ул. Сурганова, 11, 220072, Минск

пр. Независимости, 4, 220030, Минск

Viktor I. Korzyuk – Academician of the National Academy of Sciences of Belarus, Dr. Sc. (Physics and Mathematics), Professor

11, Surganov Str., 220072, Minsk

4, Nezavisimosti Ave., 220030, Minsk

https://orcid.org/0000-0002-1482-9106РудькоЯ. В.RudzkoJ. V.

Рудько Ян Вячеславович – магистр (математика и компьютерные науки), аспирант

ул. Сурганова, 11, 220072, Минск

Jan V. Rudzko – Master of Mathematics and Computer Sciences, Postgraduate Student

11, Surganov Str., 220072, Minsk

janycz@yahoo.comhttps://orcid.org/0000-0002-3773-1187КолячкоВ. В.KolyachkoV. V.

Колячко Владислав Владимирович – стажер

ул. Сурганова, 11, 220072, Минск

Vladislav V. Kolyachko – Research Intern

11, Surganov Str., 220072, Minsk

vladislav.kolyachko@gmail.comИнститут математики Национальной академии наук Беларуси; Белорусский государственный университетInstitute of Mathematics of the National Academy of Sciences of Belarus; Belarusian State UniversityИнститут математики Национальной академии наук БеларусиInstitute of Mathematics of the National Academy of Sciences of Belarus202514102025613183194Copyright © Корзюк В.И., Рудько Я.В., Колячко В.В., 20252025Корзюк В.И., Рудько Я.В., Колячко В.В.Korzyuk V.I., Rudzko J.V., Kolyachko V.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestifm.belnauka.by/jour/article/view/848

Изучается смешанная задача для одномерного волнового уравнения в криволинейной полуполосе. Начальные условия имеют разрыв первого рода в одной точке. Смешанная задача моделирует задачу о продольном ударе по конечному упругому стержню с подвижной границей. С использованием метода характеристик получено решение в явном аналитическом виде. Для рассматриваемой задачи доказывается единственность решения и устанавливаются условия, при которых существует ее классическое решение.

We study a mixed problem for a one-dimensional wave equation in a curvilinear half-strip. The initial conditions have a discontinuity of the first kind at a single point. The mixed problem models the problem of a longitudinal impact on a finite elastic rod with a movable boundary. Using the method of characteristics, we obtain the solution in an explicit analytical form. For the problem in question, we prove the uniqueness of the solution and establish the conditions under which its classical solution exists.

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