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

## DOI:

https://doi.org/10.17721/1812-5409.2020/3.11## Abstract

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 - 109

** Language of the article**: Ukrainian

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*Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics*, (3), 103–109. https://doi.org/10.17721/1812-5409.2020/3.11

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