TITLE:
The Cauchy Problem for the Heat Equation with a Random Right Part from the Space Subφ (Ω)
AUTHORS:
Yuriy Kozachenko, Anna Slyvka-Tylyshchak
KEYWORDS:
Cauchy Problem, Heat Equation, Stochastic Process
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.15,
August
19,
2014
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 Subφ (Ω). Estimation for the distribution of the supremum
of solutions of such equations is founded.