The Cauchy Problem for the Heat Equation with a Random Right Part from the Space Sub_φ (Ω)

Yuriy Kozachenko, Anna Slyvka-Tylyshchak

Department of Probability Theory, Statistics and Actuarial Mathematics, The Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine.

DOI: 10.4236/am.2014.515226                

Abstract

The influence of random factors should often be taken into account in solving problems of mathematical physics. The heat equation with random factors is a classical problem of the parabolic type of mathematical physics. In this paper, the heat equation with random right side is examined. In particular, we give conditions of existence with probability, one classical solutions in the case when the right side is a random field, sample continuous with probability one from the space Sub_φ (Ω). Estimation for the distribution of the supremum of solutions of such equations is founded.

Keywords

Cauchy Problem, Heat Equation, Stochastic Process

Conflicts of Interest

The authors declare no conflicts of interest.

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