Multiscale convergence and reiterated homogenization of parabolic problems

Holmbom, Anders; Svanstedt, Nils; Wellander, Niklas

doi:10.1007/s10492-005-0009-z

Cited by 31 publications

(28 citation statements)

References 5 publications

(9 reference statements)

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“…In [9] it is proven that for a bounded sequence {u ε } in H 1 (Ω) and with u and u 1 defined as in Theorem 3 it holds that, up to a subsequence,…”

Section: Two-scale Convergence and Asymptotic Expansionsmentioning

confidence: 99%

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Homogenization of some parabolic operators with several time scales

Flodén

Olsson

2007

Appl Math

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“…In [9] it is proven that for a bounded sequence {u ε } in H 1 (Ω) and with u and u 1 defined as in Theorem 3 it holds that, up to a subsequence,…”

Section: Two-scale Convergence and Asymptotic Expansionsmentioning

confidence: 99%

“…The corresponding results for nonlinear problems are obtained in [16]. In [9] reiterated homogenization results for linear parabolic operators are proven by means of multiscale convergence methods.…”

Section: Homogenizationmentioning

confidence: 99%

Homogenization of some parabolic operators with several time scales

Flodén

Olsson

2007

Appl Math

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“…In the present work, we will deal with the following time-dependent version of multiscale convergence It has been for the first time considered by Holmbom [9] (see also [10,41,42]). It reads as: A sequence (u ε ) ε>0 ⊂ L p (Q) (Q = Ω × (0, T ),…”

Section: Multiscale Convergence and Related Convolution Resultsmentioning

confidence: 99%

Multiscale nonlocal flow in a fractured porous medium

Woukeng

2014

Ann Univ Ferrara

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Abstract. We study the flow generated by an incompressible viscoelastic fluid in a fractured porous medium. The model consists of a fluid flow governed by Stokes-Volterra equations evolving in a periodic double-porosity medium. Using the multiscale convergence method associated to some recent tools about the convergence of convolution sequences, we show that the equivalent macroscopic model is of the same type as the microscopic one, but in a fixed domain.

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“…Furthermore, the (homogenized) coefficients of L 0 as well as the first-order correctors depend on k, but only for three separated cases: 0 < k < 2; k = 2; and 2 < k < ∞. For more recent work on multiscale convergence and reiterated homogenization, see [1,18,12,23,26] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Homogenization of Parabolic Equations with Non-self-similar Scales

Geng¹,

Shen²

2019

Arch Rational Mech Anal

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This paper is concerned with quantitative homogenization of second-order parabolic systems with periodic coefficients varying rapidly in space and time, in different scales. We obtain large-scale interior and boundary Lipschitz estimates as well as interior C 1,α and C 2,α estimates by utilizing higher-order correctors. We also investigate the problem of convergence rates for initial-boundary value problems.MSC2010: 35B27, 35K40.

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Multiscale convergence and reiterated homogenization of parabolic problems

Cited by 31 publications

References 5 publications

Homogenization of some parabolic operators with several time scales

Homogenization of some parabolic operators with several time scales

Multiscale nonlocal flow in a fractured porous medium

Homogenization of Parabolic Equations with Non-self-similar Scales

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