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