The Cauchy problem for a stochastic parabolic equation with a deviation of the argument / Perun, / Yasynskyy. (2022)
Ukrainian

English  Cybernetics and Systems Analysis   /     Issue (2022, 58 (6))

Perun G., Yasynskyy V.
The Cauchy problem for a stochastic parabolic equation with a deviation of the argument

The Cauchy problem for a stochastic nonlinear equation of parabolic type with delay is considered. Using Green’s function, a formula is derived for finding the solution of the problem by the method of steps. The existence of a solution is established with probability one and the solution is estimated according to a specially introduced norm. © 2023, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: Cauchy problem, Fourier transform, Green’s function, step method, stochastic parabolic equation, Fourier transforms, Partial differential equations, Stochastic systems, Cauchy problems, Existence of a solutions, Green’s function, Parabolics, S function, Step method, Stochastic parabolic equation, Stochastics, Nonlinear equations


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Cite:
Perun G., Yasynskyy V. (2022). The Cauchy problem for a stochastic parabolic equation with a deviation of the argument. Cybernetics and Systems Analysis, 58 (6), 114–119. doi: https://doi.org/10.1007/s10559-023-00529-7 http://jnas.nbuv.gov.ua/article/UJRN-0001368555 [In Ukrainian].


 

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