Сlassical solution of the mixed problem for the one-dimensional wave equation with the nonsmooth second initial condition
https://doi.org/10.29235/1561-8323-2020-64-6-657-662
Abstract
In this article, we study the classical solution of the mixed problem in a quarter of a plane and a half-plane for a one-dimensional wave equation. On the bottom of the boundary, Cauchy conditions are specified, and the second of them has a discontinuity of the first kind at one point. Smooth boundary condition is set at the side boundary. The solution is built using the method of characteristics in an explicit analytical form. Uniqueness is proved and conditions are established under which a piecewise-smooth solution exists. The problem with linking conditions is considered.
About the Authors
V. I. Korzyuk
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Korzyuk Viktor I. – Academician, D. Sc. (Physics and Mathematics), Professor, Chief researcher
11, Surganov Str., 220072, Minsk
J. V. Rudzko
Belarusian State University
Belarus
Belarus
Rudzko Jan V. – Master student
4, Nezavisimosti Ave., 220030, Minsk
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