Existence of Solution of the Dirichlet Problem for the Heat-Conduction Equation with General Stochastic Measure
- 13 Downloads
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.
Unable to display preview. Download preview PDF.
- 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.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.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
- 6.S. D. Ivasishen, Linear Parabolic Boundary-Value Problems [in Russian], Vyshcha Shkola, Kiev (1987).Google Scholar