The conditions of existence with probability one of generalized solutions of Cauchy problem for the heat equation with a random right part

Slyvka-Tylyshchak, A. I. (2018). The conditions of existence with probability one of generalized solutions of Cauchy problem for the heat equation with a random right part. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics(4), 42–49. https://doi.org/10.17721/1812-5409.2018/4.6

The subject of this work is at the intersection of two branches of mathematics: mathematical physics and stochastic processes. The influence of random factors should often be taken into account in solving problems of mathematical physics. The heat equation with random conditions is a classical problem of mathematical physics. In this paper we consider a Cauchy problem for the heat equations with a random right part. We study the inhomogeneous heat equation on a line with a random right part. We consider the right part as a random function of the space Sub?(?). The conditions of existence with probability one generalized solution of the problem are investigated.Using this results one can construct modeless, which approximate solutions of such equations with given accuracy and reliability in the uniform metric.Key words: Sub?(?) stochastic processes, heat equation, generalized solution.Pages of the article in the issue: 42 - 49Language of the article: English