The classical solution of one problem of an absolutely inelastic impact on a long elastic semi-infinite bar
https://doi.org/10.29235/1561-2430-2021-57-4-417-427
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 boundary, the Cauchy conditions are specified, meanwhile, the second of them has a discontinuity of the first kind at one point. The smooth boundary condition, which has the first and the second order derivatives, 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 are established under which a piecewise-smooth solution exists. The problem with matcing 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, Dr. Sc. (Physics and Mathematics), Professor
11, Surganov Str., 220072, Minsk; 4, Nezavisimosti Ave., 220030
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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