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

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

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Kozachenko, Y. and Slyvka-Tylyshchak, A. (2014) The Cauchy Problem for the Heat Equation with a Random Right Part from the Space *Sub*_{φ} (Ω). *Applied Mathematics*, **5**, 2318-2333. doi: 10.4236/am.2014.515226.

Conflicts of Interest

The authors declare no conflicts of interest.

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