title: Stability of weak solutions of parabolic systems with distributed parameters on the graph
metadata.name: dc.contributor.author
metadata.value: Zhabko, Aleksei P.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Shindyapin, Andrey I.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Provotorov, Vyacheslav V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-03-05T11:54:31Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-03-05T11:54:31Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Zhabko A. P., Shindyapin A. I., Provotorov V. V. Stability of weak solutions of parabolic systems with distributed parameters on the graph. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2019, vol. 15, iss. 4, pp. 457–471.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2019.404
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/17157
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The analysis of the behaviour of the evolutionary equation solution with unlimited time
  variable has been a subject of discussion in scientific circles for a long time. There are
  many practical reasons for this when the initial conditions of the equation are specified
  with a certain error: how the small changes in the initial conditions affect the behaviour
  of the solution for large values of the time. The paper uses the classical understanding of
  the stability of the solution of a differential equation or a system of equations that goes
  back to the works of A. M. Lyapunov: a solution is stable if it little changes under the
  small perturbations of the initial condition. In the work specified the stability conditions
  for the solution of an evolutionary parabolic system with distributed parameters on a
  graph describing the process of transfer of a continuous mass in a spatial network are
  indicated. The parabolic system is considered in the weak formulation: a weak solution of
  the system is a summable function that satisfies the integral form identity, which determines
  the variational formulation for the initial-boundary value problem. By going beyond the
  classical (smooth) solutions and addressing weak solutions of the problem the authors aim
  not only to describe more precisely the physical nature of the transfer processes (this takes on
  particular importance when studying the dynamics of multiphase media) but also to the path
  analysis processes in multidimensional network-like domains. The used approach is based on
  a priori estimates of the weak solution and the construction (the Fayedo—Galerkin method
  with a special basis — the system of eigenfunctions of the elliptic operator of a parabolic
  equation) of a weakly compact family of approximate solutions in the selected state space.
  The obtained results underlie the analysis of optimal control problems for differential systems
  with distributed parameters on a graph, which have interesting analogies with multiphase
  problems of multidimensional hydrodynamics.
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 15; Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: evolutionary system of parabolic type
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: a weak solution
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: stability of a weak solutions
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Stability of weak solutions of parabolic systems with distributed parameters on the graph
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 457-471.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/17157/1/457-471.pdf
resources.format: Adobe PDF
resources.size: 332,53 kB