Блочне розщеплення системи лiнiйних матричних диференцiальних рiвнянь
| Rok vydání: | 2021 |
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| Předmět: | |
| Zdroj: | Науковий вісник Ужгородського університету. Серія: Математика і інформатика, Vol 38, Iss 1, Pp 94-104 (2021) |
| ISSN: | 2708-9568 2616-7700 |
| DOI: | 10.24144/2616-7700.2021.38(1).94-104 |
| Popis: | In the mathematical description of various phenomena and processes that arise in athematical physics, electrical engineering, economics, one has to deal with matrix differential equations. Therefore, these equations are relevant both for athematicians and for specialists in other areas of natural science. This article considers a system of M linear matrix differential equations with coefficients representable as Fourier series with coefficients and frequency slowly varying in a certain sense (class F), and this system is close to a blockdiagonal system with slowly varying coefficients. A transformation with coefficients of a similar type is sought, which leads this system to a purely block-diagonal form. With respect to the coefficients of this transformation, a quasilinear system of matrix differential equations is obtained, which decomposes into M independent subsystems, each of which has the form of some auxiliary nonlinear system. For this auxiliary system, by the method of successive approximations, conditions are obtained for the existence of class F for its solutions, and then, on the basis of this result, conditions for the existence of the desired transformation are obtained. |
| Databáze: | OpenAIRE |
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