Open AccessThe Cauchy problem for the heat equation on the plane with a random right part from the Orlicz space
Author(s) -
A. I. Slyvka-Tylyshchak,
M. M. Mykhasiuk,
Pohoriliak Oleksandr
Publication year - 2020
Publication title -
vìsnik. serìâ fìziko-matematičnì nauki/vìsnik kiì̈vsʹkogo nacìonalʹnogo unìversitetu ìmenì tarasa ševčenka. serìâ fìziko-matematičnì nauki
Language(s) - English
Resource type - Journals
eISSN - 2218-2055
pISSN - 1812-5409
DOI - 10.17721/1812-5409.2020/3.11
Subject(s) - heat equation , mathematics , initial value problem , cauchy distribution , infimum and supremum , mathematical analysis , cauchy problem , plane (geometry) , space (punctuation) , geometry , computer science , operating system
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.