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dc.contributor.authorBychkov, Evgeniy ( Orcid Icon 0000-0001-6567-4434 )
dc.contributor.authorSviridyuk, Georgy ( Orcid Icon 0000-0003-0795-2277 )
dc.contributor.authorBogomolov, Alexey ( )
dc.date.accessioned2021-08-27T14:34:00Z
dc.date.available2021-08-27T14:34:00Z
dc.date.issued2021-06-09
dc.identifier.citationBychkov, E., Sviridyuk, G., & Bogomolov, A. (2021). Optimal control for solutions to Sobolev stochastic equations. Electronic Journal of Differential Equations, 2021(51), pp. 1-11.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/14461
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.en_US
dc.formatText
dc.format.extent11 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2021, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectStochastic Sobolev type equationsen_US
dc.subjectWhite noiseen_US
dc.subjectSpace of noisesen_US
dc.subjectWiener processen_US
dc.subjectAdditive white noiseen_US
dc.titleOptimal control for solutions to Sobolev stochastic equationsen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
dc.description.departmentMathematics


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