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Short Papers

On the representation of the Goursat boundary problem solution for the first order partial derivatives stochastic hyperbolic equations

K. B. Mansimov^ab, R. O. Mastaliyev<sup>ac

a</sup> Institute of Control Systems, Baku, Azerbaijan
^b Baku State University, Baku, Azerbaijan
^c Azerbaijan University, Baku, Azerbaijan

Abstract: We study the standard canonical form of a stochastic analog of a system of linear partial differential equations of first order hyperbolic type with Goursat boundary conditions. The stochastic analogue of the Riemann matrix in block form is introduced, an integral representation of the solution of the boundary value problem under consideration is obtained in an explicit integral form in terms of boundary conditions.

Keywords: linear inhomogeneous stochastic Goursat system, stochastic boundary value problem, Wiener process, explicit representation of the solution.

UDC: 517.956.3: 519.2

MSC: 60H15

Received: 18.01.2023
Revised: 23.05.2023
Accepted: 30.05.2023

DOI: 10.26516/1997-7670.2023.45.145