Solutions of problems for the wave equation with conditions on the characteristics
https://doi.org/10.29235/1561-2430-2021-57-2-148-155
Abstract
In this paper we obtain a classical solution of the one-dimensional wave equation with conditions on the characteristics for different areas this problem is considered in. The analytical solution is constructed by the method of characteristics. In addition, the uniqueness of the obtained solution is proved. The necessity and sufficiency of the matching conditions for given functions of the problem are proved. When these conditions are satisfied and the given functions are smooth enough, the classical solution of the considered problem exists.
About the Authors
V. I. Korzyuk
Belarusian State University; Institute of Mathematics of the National Academy of Sciences of Belarus
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, Republic of Belarus
4, Nezavisimosti Ave., 220030, Minsk, Republic of Belarus
O. A. Kovnatskaya
Belarusian State University
Belarus
Belarus
Olga A. Kovnatskaya – Ph. D. (Physics and Mathematics)
4, Nezavisimosti Ave., 220030, Minsk, Republic of Belarus
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