title: Multi-dimensional non-autonomous equation contaning the production of powers of partial derivatives
metadata.name: dc.contributor.author
metadata.value: Rakhmelevich, Igor V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-04-26T09:38:44Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-04-26T09:38:44Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Rakhmelevich I.V. Multi-dimensional non-autonomous equation contaning the production of powers of partial derivatives. Vestnik SPbSU. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 1, pp. 119–130.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.113
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/9505
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: We consider a class of multidimensional partial differential equations, containing the
  production of powers of partial derivatives of arbitrary order. As a result, solutions with
  additive, multiplicative and combined separation of variables are received. The family of
  pseudo-polynomial solutions which are expressed through the polynomials on independent
  variables with arbitrary coefficients is received, as well as functions which are the solutions
  of some ordinary differential equations. The solutions of travelling wave type and selfsimilar
  solutions are founded. Also the families of solutions which have a form of the
  sum or the production of the solutions of travelling wave type and self-similar solutions
  are received. Furthermore, the solutions representing as the functions of more complicated
  arguments which are expressed through the linear combinations and the productions of
  initial independent variables are received. The conditions of existence have been formulated
  for all received solutions, and the right side of equation and its parameters must satisfy these
  conditions.
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 5(63); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: partial differential equation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: method of separation of variables
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: power-law nonlinearity
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: solution of travelling wave type
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: self-similar solution
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: pseudo-polynomial solution
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Multi-dimensional non-autonomous equation contaning the production of powers of partial derivatives
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 13-Rakhmelevich.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/9505/1/13-Rakhmelevich.pdf
resources.format: Adobe PDF
resources.size: 302,22 kB