title: Optimal control of thermal and wave processes in composite materials
metadata.name: dc.contributor.author
metadata.value: Zhabko, Aleksei P.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Karelin, Vladimir V.
metadata.lang: -
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.date.accessioned
metadata.value: 2023-10-23T18:18:59Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2023-10-23T18:18:59Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2023-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Zhabko A. P., Karelin V. V., Provotorov V. V., Sergeev S. M. Optimal control of thermal and wave processes in composite materials. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2023, vol. 19, iss. 3, pp. 403–418. https://doi.org/10.21638/11701/spbu10.2023.308 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2023.308
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/44293
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The paper indicates the approach and the corresponding him method of penalty functions
  for analyzing the problems of optimal control of thermal and wave processes in structural
  elements made of composite materials (composites). An object that is quite common in the
  industrial sphere, the structure of which is a set of layers (phases) of unidirectional composites
  — layered composites, is considered. When solving problems related to the analysis
  and description of the states of composites, quantitative characteristics of layers that are not
  functions of the coordinates of the points of the medium are usually used in order not to solve
  the corresponding problems for an inhomogeneous medium. Such functions are elements of
  Sobolev spaces, first of all, functions summable with a square. The convenience lies in the
  fact that when finding the conditions for solvability of initial-boundary value problems of
  various types (in most cases, such problems are the basis of mathematical models of many
  physical processes), it is possible to reduce to operator-difference systems, for which it is
  easy to construct a priori estimates of weak solutions. The next step after establishing the
  weak solvability of the initial-boundary value problem of the thermal or wave process in
  composites is the formulation and solution of the problem of optimal control of these processes.
  The proposed method of penalty functions on the example of solving such problems
  is a general method. It is applicable with slight modifications also not only in the case of
  elliptic, parabolic and other problems (including nonlinear) for scalar functions, but also
  for vector functions. An example of the latter is the Navier—Stokes system, widely used in
  the description of network-like hydrodynamic processes, considered in Sobolev spaces, the
  elements of which are functions with carriers on n-dimensional network-like domains, n ⩾ 2.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
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 19; Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: composite materials
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: layered region
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: initial-boundary value problem
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: weak solvability
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: optimal control
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: method of penalty functions
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Optimal control of thermal and wave processes in composite materials
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 08.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/44293/1/08.pdf
resources.format: Adobe PDF
resources.size: 293,39 kB