Previous |  Up |  Next


Title: Multiscale convergence and reiterated homogenization of parabolic problems (English)
Author: Holmbom, Anders
Author: Svanstedt, Nils
Author: Wellander, Niklas
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 50
Issue: 2
Year: 2005
Pages: 131-151
Summary lang: English
Category: math
Summary: Reiterated homogenization is studied for divergence structure parabolic problems of the form $\partial u_{\varepsilon }/\partial t - \div \bigl (a\bigl (x,x/\varepsilon ,x/\varepsilon ^2, t,t/\varepsilon ^{k}\bigr )\nabla u_{\varepsilon }\bigr )=f$. It is shown that under standard assumptions on the function $a(x,y_1,y_2,t,\tau )$ the sequence $\lbrace u_\epsilon \rbrace $ of solutions converges weakly in $L^2(0,T;H^1_0(\Omega ))$ to the solution $u$ of the homogenized problem $\partial u/\partial t -\div (b(x,t)\nabla u)=f$. (English)
Keyword: reiterated homogenization
Keyword: multiscale convergence
Keyword: parabolic equation
MSC: 35B27
MSC: 35K20
idZBL: Zbl 1099.35011
idMR: MR2125155
DOI: 10.1007/s10492-005-0009-z
Date available: 2009-09-22T18:21:20Z
Last updated: 2020-07-02
Stable URL:
Reference: [1] G.  Allaire, M.  Briane: Multiscale convergence and reiterated homogenisation.Proc. R. Soc. Edinb. 126 (1996), 297–342. MR 1386865, 10.1017/S0308210500022757
Reference: [2] M  Avellaneda: Iterated homogenization, differential effective medium theory and applications.Commun. Pure Appl. Math. 40 (1987), 527–554. Zbl 0629.73010, MR 0896766, 10.1002/cpa.3160400502
Reference: [3] A.  Bensoussan, J.-L.  Lions, and G.  Papanicolaou: Asymptotic Analysis for Periodic Structures.North-Holland, Amsterdam-New York-Oxford, 1978. MR 0503330
Reference: [4] D  Cioranescu, P.  Donato: An Introduction to Homogenization. Oxford Lecture Series in Mathematics and its Applications.Oxford Univ. Press, New York, 1999. MR 1765047
Reference: [5] A.  Dall’Aglio, F.  Murat: A corrector result for $H$-converging parabolic problems with time-dependent coefficients. Dedicated to Ennio De Giorgi.Ann. Sc. Norm. Super. Pisa Cl. Sci.  IV 25 (1997), 329–373. MR 1655521
Reference: [6] A  Holmbom: Homogenization of parabolic equations—an alternative approach and some corrector-type results.Appl. Math. 42 (1997), 321–343. Zbl 0898.35008, MR 1467553, 10.1023/A:1023049608047
Reference: [7] J.-L.  Lions, D.  Lukkassen, L. E.  Persson, and P.  Wall: Reiterated homogenization of nonlinear monotone operators.Chin. Ann. Math. Ser.  B 22 (2001), 1–12. MR 1823125, 10.1142/S0252959901000024
Reference: [8] N.  Svanstedt, N.  Wellander: A note on two-scale convergence of differential operators.Submitted.
Reference: [9] R.  Temam: Navier-Stokes equations. Theory and Numerical Analysis.North-Holland, Amsterdam-New York-Oxford, 1977. Zbl 0383.35057, MR 0609732


Files Size Format View
AplMat_50-2005-2_6.pdf 381.8Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo