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Matem. Mod., 2003, Volume 15, Number 9, Pages 17–28 (Mi mm394)  

This article is cited in 3 scientific papers (total in 3 papers)

On one mathematical model of substance transfer in fractal media

L. I. Serbina

Scientific Research Institute of Applied Mathematics and Automation, Kabardino-Balkar Scientific Centre of the Russian Academy of Sciences

Abstract: Qualitatively new mathematical model of finite-size waves propagation in semi-boundless channel filled with liquid or gas and having flat parallel walls, which are surrounded by fractal media. For this model, which is a one-dimensional wave equation with fractional sum of $3/2$ order, existence of singular solution is proved. Co-structural form of this solution is established by Fourier method. Solution of Cauchy problem for this model is found by integral equations method for the case when the speed of filtration changes according to law which considers the effects of the filtration processes in fractal media.

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Bibliographic databases:
UDC: 301+51.77
Received: 20.03.2002

Citation: L. I. Serbina, “On one mathematical model of substance transfer in fractal media”, Matem. Mod., 15:9 (2003), 17–28

Citation in format AMSBIB
\Bibitem{Ser03}
\by L.~I.~Serbina
\paper On one mathematical model of substance transfer in fractal media
\jour Matem. Mod.
\yr 2003
\vol 15
\issue 9
\pages 17--28
\mathnet{http://mi.mathnet.ru/mm394}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2025704}
\zmath{https://zbmath.org/?q=an:1048.76056}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. Yu. Bedanokova, “Matematicheskoe modelirovanie solevogo rezhima pochv s fraktalnoi strukturoi”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 2(15) (2007), 102–109  mathnet  crossref
    2. Berdyshev A.S., Kadirkulov B.J., Nieto J.J., “Solvability of An Elliptic Partial Differential Equation With Boundary Condition Involving Fractional Derivatives”, Complex Var. Elliptic Equ., 59:5 (2014), 680–692  crossref  mathscinet  zmath  isi  elib  scopus
    3. Muratbekova M.A., Shinaliyev K.M., Turmetov B.K., “On Solvability of a Nonlocal Problem For the Laplace Equation With the Fractional-Order Boundary Operator”, Bound. Value Probl., 2014, 29  crossref  mathscinet  zmath  isi  elib  scopus
  • Математическое моделирование
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