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Sbornik: Mathematics, 2010, Volume 201, Issue 1, Pages 57–77
DOI: https://doi.org/10.1070/SM2010v201n01ABEH004065
(Mi sm6377)
 

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

On repeated concentration and periodic regimes with anomalous diffusion in polymers

D. A. Vorotnikov

Voronezh State University
References:
Abstract: Spreading of a penetrant in a polymer often disagrees with the classical diffusion equations and requires that relaxation (viscoelastic) properties of polymers be taken into account. We study the boundary-value problem for a system of equations modelling such anomalous diffusion in a bounded space domain. It is demonstrated that for a sufficiently short interval of time and a fixed stress at the beginning of this interval there exists a time-global weak solution of the boundary-value problem (that is, a concentration-stress pair) such that the concentrations at the beginning and the end of the interval of time coincide. Under an additional constraint imposed on the coefficients time-periodic weak solutions (without any limits on the period length) are shown to exist.
Bibliography: 28 titles.
Keywords: non-Fickian diffusion, polymer, penetrant, topological degree, weak solution, periodicity.
Received: 07.06.2008 and 31.03.2009
Bibliographic databases:
UDC: 517.958:[536.2+539.219.3]
MSC: 35Q35, 76R50, 82D60
Language: English
Original paper language: Russian
Citation: D. A. Vorotnikov, “On repeated concentration and periodic regimes with anomalous diffusion in polymers”, Sb. Math., 201:1 (2010), 57–77
Citation in format AMSBIB
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\paper On repeated concentration and periodic regimes with anomalous diffusion in polymers
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\vol 201
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\pages 57--77
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Linking options:
  • https://www.mathnet.ru/eng/sm6377
  • https://doi.org/10.1070/SM2010v201n01ABEH004065
  • https://www.mathnet.ru/eng/sm/v201/i1/p59
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:786
    Russian version PDF:216
    English version PDF:12
    References:67
    First page:18
     
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