title: Countable stability of a weak solution of a parabolic differential-difference system with distributed parameters on the graph
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.contributor.author
metadata.value: Hoang, Van Nguyen
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2021-01-19T13:26:27Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2021-01-19T13:26:27Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Provotorov V. V., Sergeev S. M., Hoang V. N. Countable stability of a weak solution of a parabolic differential-difference system with distributed parameters on the graph. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2020, vol. 16, iss. 4, pp. 402–414.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2020.405
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/22455
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The article proposes an analog of E. Rothe’s method (semi-discretization with respect to the
  time variable) for construction convergent different schemes when analyzing the countable
  stability of a weak solution of an initial boundary value problem of the parabolic type with
  distributed parameters on a graph in the class of summable functions. The proposed method
  leads to the study of the input initial boundary value problem to analyze the boundary
  value problem in a weak setting for elliptical type equations with distributed parameters
  on the graph. By virtue of the specifics of this method, the stability of a weak solution is
  understood in terms of the spectral criterion of stability (Neumann’s countable stability),
  which establishes the stability of the solution with respect to each harmonic of the generalized
  Fourier series of a weak solution or a segment of this series. Thus, there is another possibility
  indicated, in addition to the Faedo—Galerkin method, for constructing approaches to the
  desired solution of the initial boundary value problem, to analyze its stability and the way
  to prove the theorem of the existence of a weak solution to the input problem. The approach
  is applied to finding sufficient conditions for the countable stability of weak solutions to other
  initial boundary value problems with more general boundary conditions — in which elliptical
  equations are considered with the boundary conditions of the second or third type. Further
  analysis is possible to find the conditions under which Lyapunov stability is established.
  The approach can be used to analyze the optimal control problems, as well as the problems
  of stabilization and stability of differential systems with delay. Presented method of finite
  difference opens new ways for approximating the states of a parabolic system, analyzing their
  stability in the numerical implementation and algorithmization of optimal control problems.
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 16; Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: parabolic differential-difference system
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: distributed parameters on the graph
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: weak solution
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: countable stability
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Countable stability of a weak solution of a parabolic differential-difference system with distributed parameters on the graph
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 402-414.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/22455/1/402-414.pdf
resources.format: Adobe PDF
resources.size: 264,62 kB