title: Unique weak solvability of a nonlinear initial boundary value problem with distributed parameters in a netlike domain
metadata.name: dc.contributor.author
metadata.value: Provotorov, Vyacheslav V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Ryazhskikh, Viktor I.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Gnilitskaya, Yuliya A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2017-10-12T09:41:36Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-10-12T09:41:36Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2017-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Provotorov V. V., Ryazhskikh V. I., Gnilitskaya Yu. A. Unique weak solvability of a nonlinear initial boundary value problem with distributed parameters in a netlike domain. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2017, vol. 13, iss. 3, pp. 264–277.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu10.2017.304
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/8512
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: This paper considers a fairly wide range of issues related to the solvability of the initial boundary
  value problem of the Navier—Stokes equations with distributed parameters on the net like
  region of the space Rn (n   2). The authors here develop an idea, advanced in their work for
  the case of n = 1 (the problems with distributed parameters on the graph), in the direction
  of the dimension increase n and in forming the correct Hadamard conditions for the studied
  initial boundary value problem. The general scheme of the study is classical: the problem is
  solved in the functional space which is selected (the space of feasible solutions) and a special
  basis is formed for it, the problem of approximate solutions is settled by the Faedo—Galerkin
  method, for which a priori estimates of the energy inequalities type are set and the weak
  compactness of the family of these solutions is shown based on these estimates. Using nonburdensome
  conditions, the smoothness of the solution to the time variable is demonstrated.
  The uniqueness of the weak solution is shown in the particular case n = 2, a feature quite
  often encountered in practice. The estimate for the norm of weak solution makes it possible to
  establish the continuous dependence of the weak solution from the initial data of the problem.
  The results obtained in this way are of interest to applications in the field of fluid mechanics and
  related sections of continuum mechanics, namely for the analysis of optimum control dynamics
  problems of multiphase media. It should be noted that the methods and approaches can be
  broadly generalized and are applicable to a wide class of nonlinear problems. Refs 20.
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 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: boundary value problem
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: distributed parameters on the netlike domain
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: the existence of a weak solution
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: the uniqueness conditions
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Hadamard correctness
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Unique weak solvability of a nonlinear initial boundary value problem with distributed parameters in a netlike domain
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 04-Provotorov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/8512/1/04-Provotorov.pdf
resources.format: Adobe PDF
resources.size: 295,98 kB