Affiliation:
1. Uzhhorod National University
Abstract
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 Subφ(Ω). The conditions of existence with probability one generalized solution of the problem are investigated.
Publisher
Taras Shevchenko National University of Kyiv
Subject
Medical Assisting and Transcription,Medical Terminology
Reference12 articles.
1. ANGULO J. M., RUIZ-MEDINA M. D., ANG V. V., GRECKSCH W.(2000) “Fractional diffusion and fractional heat equation”, Adv. Appl. Probab., 32., pp. 1077–1099.
2. KOZACHENKO Yu. V., LEONENKO G. M. (2006) “ Extremal behavior of the heat random field”, Extremes, 8, pp. 191–205.
3. KOZACHENKO Yu. V., VERESH K. J. (2009) “The heat equation with random initial conditions from Orlicz space”, Teor. Imovirnost. Matem. Statist., 8, pp. 63–75.
4. RATANOV N. E., SHUHOV A. G., SUHOV Yu. M. (1991) “Stabilization of the statistical solution of the parabolic equation” , Acta Appl. Math., 22, pp. 103–115.
5. KOZACHENKO Yu. V., SLYVKA-TYLYSHCHAK A. I. (2014) “The Cauchy problem for the heat equation with a random right part from the space Subφ(Ω)”, Applied Mathematics, 5, pp. 2318–2333.