Journal of Mathematical Sciences

, Volume 240, Issue 3, pp 249–255 | Cite as

Existence of Solution of the Dirichlet Problem for the Heat-Conduction Equation with General Stochastic Measure

  • M. F. Horodnii

We present sufficient conditions for the existence of a weak solution of the Dirichlet problem for the heat-conduction equation with random action described by an integral over the general stochastic measure.


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  1. 1.
    A. M. Samoilenko and O. M. Stanzhyts’kyi, Qualitative and Asymptotic Analysis of Differential Equations with Random Perturbations [in Ukrainian], Naukova Dumka, Kyiv (2009).Google Scholar
  2. 2.
    M. F. Horodnii and D. M. Polyulya, “Existence of solution of the Neumann problem for the heat-conduction equation with general stochastic measure,” Nelin. Kolyv., 18, No. 2, 192–199 (2015); English translation : J. Math. Sci., 217, No. 4, 418–426 (2016).Google Scholar
  3. 3.
    V. N. Radchenko, “Heat-conduction equation and wave equation with general stochastic measures,” Ukr. Mat. Zh., 60, No. 12, 1675–1685 (2008); English translation : Ukr. Math. J., 60, No. 12, 1968–1981 (2008).Google Scholar
  4. 4.
    V. I. Klyatskin, Stochastic Equations Through the Eyes of Physicist [in Russian], Fizmatlit, Moscow (2001).zbMATHGoogle Scholar
  5. 5.
    A. Sturm, “On convergence of population processes in random environments to the stochastic heat equation with colored noise,” Electron. J. Probab., 8, No. 6, 1–39 (2003).MathSciNetzbMATHGoogle Scholar
  6. 6.
    S. D. Ivasishen, Linear Parabolic Boundary-Value Problems [in Russian], Vyshcha Shkola, Kiev (1987).Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • M. F. Horodnii
    • 1
  1. 1.Shevchenko Kyiv National UniversityKyivUkraine

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