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Homogenization of l...
Homogenization of linear parabolic equations with three spatial and three temporal scales for certain matching between the microscopic scales
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- Danielsson, Tatiana (author)
- Mittuniversitetet,Institutionen för matematik och ämnesdidaktik
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- Johnsen, Pernilla (author)
- Mittuniversitetet,Institutionen för matematik och ämnesdidaktik
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(creator_code:org_t)
- 2021
- 2021
- English.
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In: Mathematica Bohemica. - 0862-7959 .- 2464-7136. ; 146:4, s. 483-511
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Abstract
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- In this paper we establish compactness results of multiscale and very weak multiscale type for sequences bounded in L2 (0, T; H10 (Ω)), fulfilling a certain condition. We apply the results in the homogenization of the parabolic partial differential equation εp ∂t uε(x, t) − ∇ · (a(xε−1, xε−2, tε−q, tε−r)∇uε(x, t)) = f(x, t), where 0 < p < q < r. The homogenization result reveals two special phenomena, namely that the homogenized problem is elliptic and that the matching for which the local problem is parabolic is shifted by p, compared to the standard matching that gives rise to local parabolic problems.
Subject headings
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Publication and Content Type
- ref (subject category)
- art (subject category)
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