Optimal control for solutions to Sobolev stochastic equations

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dc.contributor.authorBychkov, Evgeniy
dc.contributor.authorSviridyuk, Georgy
dc.contributor.authorBogomolov, Alexey
dc.date.accessioned2021-08-27T14:34:00Z
dc.date.available2021-08-27T14:34:00Z
dc.date.issued2021-06-09
dc.description.abstractThis 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.
dc.description.departmentMathematics
dc.formatText
dc.format.extent11 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationBychkov, E., Sviridyuk, G., & Bogomolov, A. (2021). Optimal control for solutions to Sobolev stochastic equations. <i>Electronic Journal of Differential Equations, 2021</i>(51), pp. 1-11.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/14461
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2021, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectStochastic Sobolev type equations
dc.subjectWhite noise
dc.subjectSpace of noises
dc.subjectWiener process
dc.subjectAdditive white noise
dc.titleOptimal control for solutions to Sobolev stochastic equations
dc.typeArticle

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