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Verfasst von:Trucu, Dumitru [VerfasserIn]   i
 Chaplain, Mark [VerfasserIn]   i
 Marciniak-Czochra, Anna [VerfasserIn]   i
Titel:Three-scale convergence for processes in heterogeneous media
Verf.angabe:D. Trucu, M.A.J. Chaplain, A. Marciniak-Czochra
Umfang:23 S.
Fussnoten:Published online: 15 Apr 2011 ; Gesehen am 16.08.2017
Titel Quelle:Enthalten in: Applicable analysis
Jahr Quelle:2012
Band/Heft Quelle:91(2012), 7, S. 1351-1373
ISSN Quelle:1563-504X
Abstract:In this article, we propose a new notion of multiscale convergence, called ‘three-scale’, which aims to give a topological framework in which to assess complex processes occurring at three different scales or levels within a heterogeneous medium. This generalizes and extends the notion of two-scale convergence, a well-established concept that is now commonly used for obtaining an averaged, asymptotic value (homogenization) of processes that exist on two different spatial scales. The well-posedness of this new concept is justified via a compactness theorem which ensures that all bounded sequences in L 2(Ω) are relative compact with respect to the three-scale convergence. This is taken further by giving a boundedness characterization of three-scale convergent sequences and is then continued with the introduction of the notion of ‘strong three-scale convergence’ whose well-posedness is also discussed. Finally, the three-scale convergence of the gradients is established.
DOI:doi:10.1080/00036811.2011.569498
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Verlag: http://dx.doi.org/10.1080/00036811.2011.569498
 Verlag: http://www.tandfonline.com/doi/full/10.1080/00036811.2011.569498?scroll=top&needAccess=true
 DOI: https://doi.org/10.1080/00036811.2011.569498
Datenträger:Online-Ressource
Sprache:eng
K10plus-PPN:1562459406
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