title: The method of penalty functions in the analysis of optimal control problems of Navier — Stokes evolutionary systems with a spatial variable in a network-like domain
metadata.name: dc.contributor.author
metadata.value: Zhabko, Nataliya A.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Karelin, Vladimir V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Provotorov, Vyacheslav V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Sergeev, Sergey M.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2023-08-22T10:17:17Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2023-08-22T10:17:17Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2023-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Zhabko N. A., Karelin V. V., Provotorov V. V., Sergeev S. M. The method of penalty functions in the analysis of optimal control problems of Navier — Stokes evolutionary systems with a spatial variable in a network-like domain. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2023, vol. 19, iss. 2, pp. 162–175.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2023.203
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/43825
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The article considers the Navier — Stokes evolutionary differential system used in the mathematical description of the evolutionary processes of transportation of various types of liquids through network or main pipelines. The Navier—Stokes system is considered in Sobolev spaces, the elements of which are functions with carriers on n-dimensional networklike domains. These domains are a totality of a finite number of mutually non-intersecting subdomains connected to each other by parts of the surfaces of their boundaries like a graph (in applications these are the places of branching of pipelines). Two main questions of analysis are discussed: the weak solvability of the initial boundary value problem of the Navier — Stokes system and the optimal control of this system. The main method of research of weak solutions is the semidigitization of the input system by a time variable, that is the reduction of a differential system to a differential-difference system, and using a priori estimates for weak solutions of boundary value problems to prove the theorem of the existence of a solution of the input differential system. For the optimal control problem a minimizing functional (the penalty function) and a family of the approximate functional with parameters that characterize the “penalty” for failure to fulfill the equations of state of the system are introduced. At the same time, a special Hilbert space is created, the elements of which are pairs of functions that describe the state of the system and controlling actions. The convergence of the sequence of such functions to the optimal state of the system and its corresponding optimal control is proved. The latter essentially widen the possibilities of analysis of stationary and nonstationary network-like processes of hydrodynamics and optimal control of these processesd.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: en
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Applied Mathematics. Computer Science. Control Processes;volume 19
metadata.lang: -
metadata.name: dc.subject
metadata.value: evolutionary Navier — Stokes system
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: network-like domain
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: solvability
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: optimal control
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: penalty functions
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: The method of penalty functions in the analysis of optimal control problems of Navier — Stokes evolutionary systems with a spatial variable in a network-like domain
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 03.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/43825/1/03.pdf
resources.format: Adobe PDF
resources.size: 460,7 kB