title: Optimal control of the linearized Navier— Stokes system in a netlike domain
metadata.name: dc.contributor.author
metadata.value: Provotorov, Vyacheslav V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Provotorova, Elena N.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-01-31T09:17:51Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-01-31T09:17:51Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2017-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Provotorov V. V., Provotorova E. N. Optimal control of the linearized Navier— Stokes system in a netlike domain. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2017, vol. 13, iss. 4, pp. 431–443.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu10.2017.409
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/9052
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: This work is a natural extension of research into optimal control problems of evolution equations
  with distributed parameters on a geometrical graph (network) of one of the authors in the
  direction of increasing the dimension of a spatial variable and the functions describing the
  state of the study of the Navier—Stokes equations. At the same time is examined a simple
  case of the absence of convective effect (laminar flow of an incompressible viscous fluid) —
  linearized system of Navier—Stokes equations in a net-like domain. It proves unique solvability
  of the initial boundary value problem in the weak formulation which is based on the Faedo—
  Galerkin method using a special basis (the set of generalized eigenfunctions of the special
  spectral problem) and a priori estimates of norms solutions such as power inequalities. The
  proof is constructive: to construct a sequence of approximate solutions that converges weakly
  to the exact solution of the problem. Problems are analyzed with distributed and a start control
  with a final observation, widespread in applications, that provides the necessary and sufficient
  conditions for the existence of optimal controls in terms of the conjugate states of the respective
  systems. Sufficient attention is paid to the synthesis of the optimal control action, and analogues
  of established finite-dimensional case for Kalman results have been obtained. Although, the use
  of this method is demonstrated by examples of optimal control theory, this method has a highly
  susceptible to generalization and applicable to a wide class of linear problems. Refs 15.
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 13; Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: linearized Navier—Stokes system
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: net like domain
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: weak solutions
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: optimal control
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: control synthesis
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Optimal control of the linearized Navier— Stokes system in a netlike domain
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 09-Provotorov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/9052/1/09-Provotorov.pdf
resources.format: Adobe PDF
resources.size: 258,32 kB