A mixed problem for the wave equation in a curvilinear halfstrip with discontinuous initial data
https://doi.org/10.29235/1561-2430-2025-61-3-183-194
Abstract
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.
Keywords
wave equation,
mixed problem,
method of characteristics,
classical solution,
matching conditions,
conjugation conditions,
discontinuous conditions,
curvilinear domain
Supporting agencies: The research was supported by the Moscow Center for Fundamental and Applied Mathematics of M. V. Lomonosov Moscow State University under agreement № 075-15-2025-345.
About the Authors
V. I. Korzyuk
Institute of Mathematics of the National Academy of Sciences of Belarus; Belarusian State University
Belarus
Belarus
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
J. V. Rudzko
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Jan V. Rudzko – Master of Mathematics and Computer Sciences, Postgraduate Student
11, Surganov Str., 220072, Minsk
V. V. Kolyachko
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Vladislav V. Kolyachko – Research Intern
11, Surganov Str., 220072, Minsk
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