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Ufa Mathematical Journal, 2016, Volume 8, Issue 4, Pages 111–122
DOI: https://doi.org/10.13108/2016-8-4-111
(Mi ufa357)
 

This article is cited in 10 scientific papers (total in 10 papers)

Symmetry reduction and invariant solutions for nonlinear fractional diffusion equation with a source term

S. Yu. Lukashchuk

Ufa State Aviation Technical University
References:
Abstract: We consider a problem on constructing invariant solutions to a nonlinear fractional differential equations of anomalous diffusion with a source. On the base of an earlier made group classification of the considered equation, for each case in the classification we construct the optimal systems of one-dimensional subalgebras of Lie algebras of infinitesimal operators of the point transformations group admitted by the equation. For each one-dimensional subalgebra of each optimal system we find the corresponding form of the invariant solution and made the symmetry reduction to an ordinary differential equation. We prove that there are three different types of the reduction equations (factor equations): a second order ordinary differential equation integrated by quadratures and two ordinary nonlinear fractional differential equations. For particular cases of the latter we find exact solutions.
Keywords: fractional diffusion equation, symmetry, optimal system of subalgebras, symmetry reduction, invariant solution.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 11.G34.31.0042
The work is made in Ufa State Aviation Technical University in the framework of contract no. 11.G34.31.0042 by Law no. 220 of the Goverment of Russian Federation.
Received: 08.02.2016
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 45K05, 70G65
Language: English
Original paper language: Russian
Citation: S. Yu. Lukashchuk, “Symmetry reduction and invariant solutions for nonlinear fractional diffusion equation with a source term”, Ufa Math. J., 8:4 (2016), 111–122
Citation in format AMSBIB
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\by S.~Yu.~Lukashchuk
\paper Symmetry reduction and invariant solutions for nonlinear fractional diffusion equation with a~source term
\jour Ufa Math. J.
\yr 2016
\vol 8
\issue 4
\pages 111--122
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\crossref{https://doi.org/10.13108/2016-8-4-111}
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\elib{https://elibrary.ru/item.asp?id=27512569}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85013413899}
Linking options:
  • https://www.mathnet.ru/eng/ufa357
  • https://doi.org/10.13108/2016-8-4-111
  • https://www.mathnet.ru/eng/ufa/v8/i4/p114
  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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