The classical solution of the mixed problem for the one-dimensional wave equation with the nonsmooth second initial condition
https://doi.org/10.29235/1561-2430-2021-57-1-23-32
Abstract
In this article, we study the classical solution of the mixed problem in a quarter of a plane for a one-dimensional wave equation. On the bottom of the boundary, the Cauchy conditions are specified, and the second of them has a discontinuity of the first kind at a point. The smooth boundary condition is set at the side boundary. The solution is built using the method of characteristics in an explicit analytical form. The uniqueness is proved, and the conditions under which a piecewise-smooth solution exists are established. The problem with conjugate conditions is considered
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 Aca demy 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’s Degree Student, Belarusian State University
4, Nezavisimosti Ave., 220030, Minsk
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