CONSTRUCTIVE ASPECTS OF INTEGRATION. ISSUES OF THE MATERIAL INTEGRAL EQUATIONS

P. Kotov

doi:10.12737/19491

CONSTRUCTIVE ASPECTS OF INTEGRATION. ISSUES OF THE MATERIAL INTEGRAL EQUATIONS

Published in Modeling of systems and processes · Volume 8, Issue 4 · Pages 15–18 · Rubric: Tehnicheskie nauki

DOI: https://doi.org/10.12737/19491

Received: 10.05.2016 Accepted: 10.05.2016 Published: 10.05.2016 Language of publication: RUS

Authors

P. Kotov

ABSTRACT

The differential equation with the continuous disturbance effect in the right part is considered and solid approaches to the initial equation solution, to the integration of an initial problem in relation to the variant of o gravitational interaction model represented by the differential equation in a normal form are proposed.

KEYWORDS

primitive function, Cauchy problem, unique solution.

Text

I. Введение

Простейшее уравнение в нормальной форме первого порядка рассматривается таким [1]:

(В.1) $\text{[math]}$

где D - оператор дифференцирования по t (нередко такой оператор обозначается р, r). Функцию f называют неоднородностью уравнения (В.1). Решением исходного уравнения (В.1) является каждая первообразная функции f на промежутке I. Других решений уравнение (В.1) не имеет. Теорему об однозначной разрешимости задачи Коши обозначают кратко TOP [1]. Рассматривая уравнения и их решения при I=R.

1. Bogdanov Yu.S. Differentsial´nye uravneniya [Tekst] / Yu.S. Bogdanov, Yu.B. Syroid. - Mn. : Vyssh. shk., 1983. - 239 s.

2. Krasnov, M. L. Integral´nye uravneniya [Tekst] / M. L. Krasnov. - M. :Nauka, 1975. - 304 s.

3. Siama, D. Fizicheskie printsipy obshchey teorii otnositel´nosti [Tekst] / D. Siama. - M. : Mir, 1971. - 102 s.

JATS XML

Editor-in-Chief, editorial board chair

GOST

Kotov P. CONSTRUCTIVE ASPECTS OF INTEGRATION. ISSUES OF THE MATERIAL INTEGRAL EQUATIONS // Modeling of systems and processes. 2016. no. 4. pp. 15-18. DOI: https://doi.org/10.12737/19491. (Date of access 14.10.2026).

MLA

P. Kotov. "CONSTRUCTIVE ASPECTS OF INTEGRATION. ISSUES OF THE MATERIAL INTEGRAL EQUATIONS." Modeling of systems and processes 8.4 (2016): 15-18. DOI: https://doi.org/10.12737/19491.

APA

Kotov P. (2016). CONSTRUCTIVE ASPECTS OF INTEGRATION. ISSUES OF THE MATERIAL INTEGRAL EQUATIONS. Modeling of systems and processes, 8(4), 15-18. https://doi.org/10.12737/19491

Chicago

P. Kotov. "CONSTRUCTIVE ASPECTS OF INTEGRATION. ISSUES OF THE MATERIAL INTEGRAL EQUATIONS." Modeling of systems and processes 8, no. 4 (2016): 15-18. https://doi.org/10.12737/19491.

WIKI

{{cite journal | author = Kotov P. | title = CONSTRUCTIVE ASPECTS OF INTEGRATION. ISSUES OF THE MATERIAL INTEGRAL EQUATIONS | journal = Modeling of systems and processes | year = 2016 | volume = 8 | issue = 4 | pages = 15-18 | doi = 10.12737/19491 }}

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CONSTRUCTIVE ASPECTS OF INTEGRATION. ISSUES OF THE MATERIAL INTEGRAL EQUATIONS

I. Введение

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