Periodic unfolding and Robin problems in perforated domains

Cioranescu, Doina; Donato, Patrizia; Zaki, Rachad

doi:10.1016/j.crma.2006.01.028

Cited by 71 publications

(117 citation statements)

References 9 publications

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“…Using the unfolding method, [4], [6], [7], [8], [15], [18], and the structure of the equations we prove the convergence of the nonlinear terms.…”

Section: The Matricesmentioning

confidence: 94%

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Derivation of a Macroscopic Model for Transport of Strongly Sorbed Solutes in the Soil Using Homogenization Theory

Ptashnyk¹,

Roose²

2010

SIAM J. Appl. Math.

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Abstract. In this paper we derive a model for the diffusion of strongly sorbed solutes in soil taking into account diffusion within both the soil fluid phase and the soil particles. The model takes into account the effect of solutes being bound to soil particle surfaces by a reversible nonlinear reaction. Effective macroscale equations for the solute movement in the soil are derived using homogenization theory. In particular we use the unfolding method to prove the convergence of nonlinear reaction terms in our system. We use the final, homogenized model to estimate the effect of solute dynamics within soil particles on plant phosphate uptake by comparing our double-porosity model to the more commonly used single porosity model. We find that there are significant qualitative and quantitative differences in the predictions of the models. This highlights the need for careful experimental and theoretical treatment of the plant-soil interaction when trying to understand solute losses from the soil.

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“…Using the unfolding method, [4], [6], [7], [8], [15], [18], and the structure of the equations we prove the convergence of the nonlinear terms.…”

Section: The Matricesmentioning

confidence: 94%

“…Using the unfolding method, [4,6,7,8,15,18], and the structure of the equations we show in Lemma 5.4 the two-scale convergence of the nonlinear functions. The macroscopic model depends crucially on the ratio between diffusion coefficients in the inter-particle D e and intra-particle D i spaces.…”

mentioning

confidence: 97%

Derivation of a Macroscopic Model for Transport of Strongly Sorbed Solutes in the Soil Using Homogenization Theory

Ptashnyk¹,

Roose²

2010

SIAM J. Appl. Math.

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“…The statement (i) is a direct consequence of (10) while (ii)-(iv) are proved in [7,9] and (v) in [7,11]. We present here only the proof of (vi).…”

Section: Periodic Unfolding Operatormentioning

confidence: 98%

Homogenization of thin piezoelectric perforated shells

et al. 2007

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Abstract. We rigorously establish the existence of the limit homogeneous constitutive law of a piezoelectric composite made of periodically perforated microstructures and whose reference configuration is a thin shell with fixed thickness. We deal with an extension of the Koiter shell model in which the three curvilinear coordinates of the elastic displacement field and the electric potential are coupled. By letting the size of the microstructure going to zero and by using the periodic unfolding method combined with the Korn's inequality in perforated domains, we obtain the limit model.Mathematics Subject Classification. 74K25, 74Q05, 35B27.

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“…In this paper, we consider the correctors for this homogenization. The proofs mainly rely on the periodic unfolding method, which was originally introduced in Cioranescu et al [6] (see also [7]) and extended to perforated domains in Cioranescu et al [12] (see Cioranescu et al [8] for more general situations and a comprehensive presentation). Next we state our main results, in which we will use some notations to be defined in the next section.…”

Section: Introductionmentioning

confidence: 99%