Optimal control for solutions to Sobolev stochastic equations




Bychkov, Evgeniy
Sviridyuk, Georgy
Bogomolov, Alexey

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Texas State University, Department of Mathematics


This article concerns the optimal control problem for internal gravitational waves in a model with additive "white noise". This mathematical models based on the stochastic Sobolev equation, Dirichlet boundary conditions, and a Cauchy initial condition. The inhomogeneity describes random heterogeneities of the medium and fluctuations. By white noise we realize the Nelson-Gliklikh derivative of the Wiener process. The study was carried out within the framework of the theory of relatively bounded operators and the theory of Sobolev-type stochastic equations of higher order and the theory of (semi) groups of operators. We show the existence and uniqueness of a strong solutions, and obtain sufficient conditions for the existence of an optimal control of such solutions. The theorem about the existence and uniqueness of the optimal control is based on the works of J.-L. Lyons.



Stochastic Sobolev type equations, White noise, Space of noises, Wiener process, Additive white noise


Bychkov, E., Sviridyuk, G., & Bogomolov, A. (2021). Optimal control for solutions to Sobolev stochastic equations. Electronic Journal of Differential Equations, 2021(51), pp. 1-11.


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