title: On a cubic variational problem
metadata.name: dc.contributor.author
metadata.value: Malozemov, Vassili N.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Tamasyan, Grigoriy Sh.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2017-01-05T18:01:29Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-01-05T18:01:29Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2016-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Malozemov V.N., Tamasyan G. S. On a cubic variational problem. Vestnik of Saint Petersburg University. Series 1. Mathematics. Mechanics. Astronomy, 2016, vol. 3 (61), issue 4, pp. 615– 623.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2016.410
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/5901
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: An extremal curve of the simplest variational problem is a continuously differentiable function. Hilbert’s
  differentiability theorem provides a condition that guarantees the existence of the second derivative of an
  extremal curve. It is desirable to have a simple example in which the condition of Hilbert’s theorem fails
  to hold true and an extremal curve is not twice differentiable.
  In this paper, we analyse a cubic variational problem with the following properties. The functional
  of the problem is neither bounded from above nor bounded from below. There exists an extremal curve
  of this problem that is obtained by pasting together two different extremal curves, and that is not twice
  differentiable at the sewing point. Despite this unfavourable situation, an attempt to apply the method
  of steepest descent (in the form proposed by V. F. Demyanov) to this problem is made. It appears that
  the method converges to the extremal curve provided one chooses a suitable step size rule. Refs 2. Figs 6.
  Table 1.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при поддержке СПбГУ (грант №9.38.205.2014).
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. Series 1. Mathematics. Mechanics. Astronomy;Vol. 3 (61); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: cubic variational problem
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: extremal curve
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: method of steepest descent
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On a cubic variational problem
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 10-Malozemov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/5901/1/10-Malozemov.pdf
resources.format: Adobe PDF
resources.size: 277,51 kB