title: Inverse problem for non-homogeneous integro-differential equation of hyperbolic type
metadata.name: dc.contributor.author
metadata.value: Safarov, Jurabek Sh.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2024-05-30T15:41:25Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2024-05-30T15:41:25Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2024-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Safarov J. Sh. Inverse problem for non-homogeneous integro-differential equation of hyperbolic type. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2024, vol. 11 (69), issue 1, pp. 141–151. https://doi.org/10.21638/spbu01.2024.109 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2024.109
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/45456
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: An inverse problem is considered, which consists in finding a solution and a one-dimensional
  kernel of the integral term of an inhomogeneous integro-differential equation of hyperbolic
  type from the conditions that make up the direct problem and some additional condition.
  First, the direct problem is investigated, while the kernel of the integral term is assumed to
  be known. By integrating over the characteristics, the given intego-differential equation is
  reduced to a Volterra integral equation of the second kind and is solved by the method of
  successive approximations. Further, using additional information about the solution of the
  direct problem, we obtain an integral equation with respect to the kernel of the integral
  k(t), of the integral term. Thus, the problem is reduced to solving a system of integral
  equations of the Volterra type of the second kind. The resulting system is written as an
  operator equation. To prove the global, unique solvability of this problem, the method of
  contraction mappings in the space of continuous functions with weighted norms is used.
  And also the theorem of conditional stability of the solution of the inverse problem is
  proved, while the method of estimating integrals and Gronoullo’s inequality is used.
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 11 (69); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: hyperbolic type equation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: integro differential equation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: the core
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: the inverse problem
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: compressed mapping method
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Inverse problem for non-homogeneous integro-differential equation of hyperbolic type
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 141-151.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/45456/1/141-151.pdf
resources.format: Adobe PDF
resources.size: 300,49 kB