Characteristic Cauchy’s problem with prehistory in the case of nonlinear differential equations in partial derivatives

Kohutych, O. I.; Marynets, V. V.

doi:10.17721/1812-5409.2020/4.4

Characteristic Cauchy’s problem with prehistory in the case of nonlinear differential equations in partial derivatives

Тип публікації :

Стаття

Дата випуску :

2020

Автор(и) :

Kohutych, O. I.

Marynets, V. V.

Мова основного тексту :

Англійська

eKNUTSHIR URL :

https://ir.library.knu.ua/handle/15071834/26176

DOI :

10.17721/1812-5409.2020/4.4

Журнал :

Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics

Випуск :

4

ISSN :

1812-5409

Початкова сторінка :

28

Кінцева сторінка :

33

Цитування :

[APA 7] Kohutych, O. I., & Marynets, V. V. (2020). Characteristic Cauchy’s problem with prehistory in the case of nonlinear differential equations in partial derivatives. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics, (4), 28–33. https://doi.org/10.17721/1812-5409.2020/4.4

[ДСТУ] Kohutych O. I., Marynets V. V. Characteristic Cauchy’s problem with prehistory in the case of nonlinear differential equations in partial derivatives. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics. 2020. no. 4. P. 28—33. DOI: 10.17721/1812-5409.2020/4.4 (date of access: 25.07.2026).

We have built a constructive method of investigation and approximate solution for nonlinear Gursa’s problem with prehistory. We have established sufficient condition of subsistence, existence of unity and constant signs solution of the investigated problem. At mathematical description to different nature process (gas sorption, the spread of moisture in the porous substances, pipes heating by a stream of hot water, drying by the airflow, etc. [1]) we often come to boundary value problems for nonlinear differential equations in partial derivatives, when not all output data are known, that is some of them need to be found from auxiliary nonlinear problems, which are mathematical models of processes that proceeded the research. These problems should be named as problems with prehistory. One approach to investigation and approximate solution to such a problem has been proposed in the current paper.Key words: two-sided method, sufficient conditions, "free" curves, characteristic Cauchy’s problem with prehistory.Pages of the article in the issue: 28 - 33Language of the article: Ukrainian

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