A particular solution of a problem for a system of equations from mechanics with nonsmooth Cauchy condition
https://doi.org/10.29235/1561-2430-2022-58-3-300-311
Abstract
In this article, we study a mixed problem in a quarter-plane for a system of differential equations, which describes vibrations in a string from viscoelastic material, which corresponds to Maxwell material. At the bottom of the boundary, the Cauchy conditions are specified, and one of them has a discontinuity of the first kind at one point. A smooth boundary condition is set at the side boundary. The Klein – Gordon – Fock equation is derived for one of the system’s functions. We find a particular solution in two ways. The first method builds it in an explicit analytical form (with a continuation of one function), and the second one constructs it as a solution of an integral equation using the method of characteristics (without continuation of one function). Conditions are established under which the solution has sufficient smoothness.
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; 4, Nezavisimosti Ave., 220030, Minsk
J. V. Rudzko
Belarusian State University
Belarus
Belarus
an V. Rudzko – Master of Mathematics and Computer
Science
4, Nezavisimosti Ave., 220030, Minsk
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