title: On integral equations of cracks of a new type
metadata.name: dc.contributor.author
metadata.value: Babeshko, Vladimir A.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Evdokimova, Olga V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Babeshko, Olga M.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-10-19T20:09:09Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-10-19T20:09:09Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Babeshko V.A., Evdokimova O.V., Babeshko O. M. On integral equations of cracks of a new type. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2022, vol. 9 (67), issue 3, pp. 405–416. https://doi.org/10.21638/spbu01.2022.302 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2022.302
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/38283
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: For the first time, the paper develops a new type of crack modeling method that allows
  describing them in environments of complex rheologies. It is based on a new universal
  modeling method previously published by the authors, used in boundary value problems
  for systems of partial differential equations. The advantage of the method is the possibility
  of avoiding the need to solve complex boundary value problems for systems of partial
  differential equations by replacing them with separate differential equations, among which
  the Helmholtz equations are the simplest. Namely, with the help of combinations of solutions
  of boundary value problems for this equation, it is possible to describe the behavior of
  complex solutions of multicomponent boundary value problems. In this paper, for the first
  time, the method is applied to a mixed boundary value problem for cracks of a new type.
  Cracks of a new type, complementing the Griffiths cracks, were discovered during the study
  of fractures of lithospheric plates that converge at the ends during oncoming traffic along
  the Conrad boundary. In the course of the study, Kirchhoff plates were adopted as models of
  lithospheric plates. The method developed in the published article is aimed at the possibility
  of describing models of approaching objects similar to lithospheric plates in the form of
  deformable plates of more complex rheologies. In particular, it can be thermoelectroelastic
  plates or other rheology. In the process of solving problems using Kirchhoff models for
  lithospheric plates, there was a problem of calculating some functionals that needed to be
  determined. This method demonstrates an approach that eliminates this drawback. The
  derivation of integral equations of cracks of a new type, the method of their solution and
  the approach to application in more complex rheologies is given.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Some fragments of the work were completed as part of the implementation of the Russian Ministry
  of Education and Science state task for 2022 (project FZEN-2020-0020), Southern Scientific Center of the
  Russian Academy of Sciences (project 00-20-13, state registration no. 122020100341-0), and supported
  by the Russian Foundation for Basic Research (projects 19-41-230003, 19-41-230004, 19-48-230014).
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. Mathematics. Mechanics. Astronomy;Volume 9(67); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: block element
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: factorization
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: integral equations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: external forms
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: cracks of a new type
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On integral equations of cracks of a new type
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 405-416.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/38283/1/405-416.pdf
resources.format: Adobe PDF
resources.size: 321,63 kB