Abstract: The paper considers the transverse vibrations of two strings connected to each other at a certain point. A mathematical model of this process, based on the law of conservation of momentum, expressed in the form of an integro-differential equation is constructed. This equation connects the deviations of the strings during vibrations with their characteristics such as density, tension, and sources of external forces. This approach can be considered as a development of the method proposed by A.N. Tikhonov for the equation of string vibrations with nonsmooth data. For the case where the densities of the strings are constants, we set a nonclassical problem for the integro-differential equation. In addition to the Cauchy data, the problem includes necessary matching conditions. A theorem on the existence and uniqueness of a solution to the problem is proved, and explicit formulas are obtained for its solution.

Cite: Konovalova D.S.
Nonclassical Problem for Transverse Vibrations of a String System
Journal of Applied and Industrial Mathematics. 2025. V.19. N1. P.59-66. DOI: 10.1134/S1990478925010065 Scopus РИНЦ

Original: Коновалова Д.С.
Неклассическая задача для процесса поперечных колебаний системы струн
Сибирский журнал индустриальной математики. 2025. Т.28. №1. С.15-25. DOI: 10.33048/SIBJIM.2025.28.102 РИНЦ

Dates:

Submitted:	Aug 2, 2024
Accepted:	Mar 10, 2025
Published print:	Nov 2, 2025
Published online:	Nov 2, 2025

Identifiers:

Scopus:	2-s2.0-105020670467
Elibrary:	83155451

Citing: Пока нет цитирований

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