9. OPTIMAL CONTROL PROBLEM FOR ONE MATHEMATICAL MODEL OF HYDRODYNAMICS WITH

RANDOM INITIAL DATA


Author: E. YCHKOV, A. ZAMYSHLYAEVA & G. SVIRIDYUK                                            DOWNLOAD                                                                                                                                                                                                                                                                                   


How to Cite:




Bychkov, Evgeniy, Alyona Zamyshlyaeva, and Georgy Sviridyuk. "Optimal Control Problem for One Mathematical

Model of Hydrodynamics with Random Initial Data." Global and Stochastic Analysis, vol. 12, no. 5, 2025, pp. 67–78.



Abstract




The paper studies a stochastic mathematical model based on the improved modified Boussinesq equation (IMBq)

with random initial data. This equation is used to describe wave propagation in shallow water with conservation of

mass in layer and taking into account capillary effects, as well as to study deformation waves in thin elastic rods.

The time derivative is understood in the sense of the Nelson–Gliklikh derivative. A theorem on the existence and

uniqueness of a solution for an inhomogeneous equation with random initial data with zero mathematical

expectations is proved. Sufficient conditions for solving the problem of optimal control in mathematical models

with random initial data are found.



Keywords


Key words and phrases. optimal control problem; Sobolev type equations; mathematical model of wave propagation

in shallow water; Nelson-Gliklikh derivative