title: Uniqueness solution to the inverse spectral problem with distributed parameters on the graph-star
metadata.name: dc.contributor.author
metadata.value: Zhabko, Aleksei P.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Nurtazina, Karlygash B.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Provotorov, Vyacheslav V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-08-24T20:24:22Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-08-24T20:24:22Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Zhabko A. P., Nurtazina K. B., Provotorov V. V. Uniqueness solution to the inverse spectral problem with distributed parameters on the graph-star. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2020, vol. 16, iss. 2, pp. 129–143.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2020.205
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/19015
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In the space of piecewise smooth functions on a star graph, the question of the uniqueness
  of the recovery of the differential operator of a boundary value problem from its spectral
  characteristics is analyzed. The uniqueness of the recovery of the coefficient in a differential
  expression and the constant in the boundary conditions of a boundary value problem from
  spectral data is considered — a set of eigenvalues and a set of norms of the operator’s
  eigenfunctions. The operator of the boundary value problem has a singularity generated
  by the structure of the graph: differential expression is defined on the interior parts of
  all the edges of the graph, and in the interior node of the graph, where the differential
  expression loses its meaning, there is a generalized condition of Kirchhoff — the condition
  of agreement (the condition of conjugating). A spectral approach is used, which is based
  on the spectral properties of the elliptical operator: the analyticity of Green’s function of
  the boundary value problem on the spectral parameter, spectral completeness and the basis
  property of the set of its eigenfunctions in the space of square integrable function. The results
  are the basis for solving inverse problems for evolutionary differential systems of parabolic
  and hyperbolic types with distributed parameters on the network (graph), the elliptical part
  of which contains coefficients to be determined. In problems of an applied nature, these are,
  first of all, parameters that characterize the properties of the transfer of the solid environment
  and describe the elastic properties of the process of deformation of the environment. The
  approach mentioned above can also be applied to problems whose space variable is vectorlike
  and varies in a network-like domain.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work was financially supported by the Ministry of Education and Science of the Republic
  Kazakhstan (project N AP05136197).
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 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: graph
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: differential operator
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: spectral characteristics
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: inverse spectral problem
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: uniqueness solution
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Uniqueness solution to the inverse spectral problem with distributed parameters on the graph-star
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 129-143.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/19015/1/129-143.pdf
resources.format: Adobe PDF
resources.size: 302,43 kB