The Cauchy problem for the heat equation on the plane with a random right part from the Orlicz space

Slyvka-Tylyshchak, A. I.; Mykhasiuk, M. M.; Pohoriliak, O. O.

doi:10.17721/1812-5409.2020/3.11

The Cauchy problem for the heat equation on the plane with a random right part from the Orlicz space

Тип публікації :

Стаття

Дата випуску :

2020

Автор(и) :

Slyvka-Tylyshchak, A. I.

Mykhasiuk, M. M.

Pohoriliak, O. O.

Мова основного тексту :

Англійська

eKNUTSHIR URL :

https://ir.library.knu.ua/handle/15071834/26169

DOI :

10.17721/1812-5409.2020/3.11

Журнал :

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

Випуск :

3

ISSN :

1812-5409

Початкова сторінка :

103

Кінцева сторінка :

109

Цитування :

[APA 7] Slyvka-Tylyshchak, A. I., Mykhasiuk, M. M., & Pohoriliak, O. O. (2020). The Cauchy problem for the heat equation on the plane with a random right part from the Orlicz space. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics, (3), 103–109. https://doi.org/10.17721/1812-5409.2020/3.11

[ДСТУ] Slyvka-Tylyshchak A. I., Mykhasiuk M. M., Pohoriliak O. O. The Cauchy problem for the heat equation on the plane with a random right part from the Orlicz space. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics. 2020. no. 3. P. 103—109. DOI: 10.17721/1812-5409.2020/3.11 (date of access: 18.07.2026).

The heat equation with random conditions is a classical problem of mathematical physics. Recently, a number of works appeared, which in many ways investigated this equation according to the type of random initial conditions. We consider a Cauchy problem for the heat equations with a random right part. We study the inhomogeneous heat equation on the plane with a random right part. We consider the right part as a random function of the Orlicz space. The conditions of existence with probability one classical solution of the problem are investigated. For such a problem has been got the estimation for the distribution of the supremum solution.Key words: stochastic processes of the Orlicz space, heat equation, estimation for the distribution of the supremum solution.Pages of the article in the issue: 103 - 109Language of the article: Ukrainian

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