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

Anna Slyvka-Tylyshchak | Zendy; M. M. Mykhasiuk | Zendy; Pohoriliak Oleksandr | Zendy

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

Author(s) -

Anna Slyvka-Tylyshchak,

M. M. Mykhasiuk,

Pohoriliak Oleksandr

Publication year - 2020

Publication title -

bulletin of taras shevchenko national university of kyiv series physics and mathematics

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.

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