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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A. M. Samoilenko and O. M. Stanzhyts’kyi, Qualitative and Asymptotic Analysis of Differential Equations with Random Perturbations [in Ukrainian], Naukova Dumka, Kyiv (2009).
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).
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).
V. I. Klyatskin, Stochastic Equations Through the Eyes of Physicist [in Russian], Fizmatlit, Moscow (2001).
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).
S. D. Ivasishen, Linear Parabolic Boundary-Value Problems [in Russian], Vyshcha Shkola, Kiev (1987).
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Translated from Neliniini Kolyvannya, Vol. 21, No. 1, pp. 29–35, January–February, 2018.
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Horodnii, M.F. Existence of Solution of the Dirichlet Problem for the Heat-Conduction Equation with General Stochastic Measure. J Math Sci 240, 249–255 (2019). https://doi.org/10.1007/s10958-019-04351-5
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DOI: https://doi.org/10.1007/s10958-019-04351-5