A particular solution of a problem for a system of equations from mechanics with nonsmooth Cauchy condition
| Autor: | V. I. Korzyuk, J. V. Rudzko |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series. 58:300-311 |
| ISSN: | 2524-2415 1561-2430 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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