Homogenization of Richards' equations in multiscale porous media with soft inclusions

Jäger, Willi; Woukeng, Jean Louis

doi:10.1016/j.jde.2021.02.012

Cited by 7 publications

(6 citation statements)

References 34 publications

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“…), no scaling is needed in the left-hand side of (18). Now, for (15), we follow exactly the same lines of reasoning as in [2] to obtain it.…”

Section: Well Posedness and Uniform Estimatesmentioning

confidence: 96%

“…Therefore, by integrating ( 19) over (0, t) (t ∈ (0, T]) and taking into account (18) and ( 20), we are led to…”

Section: Well Posedness and Uniform Estimatesmentioning

confidence: 99%

“…We also need an estimate of ∂u ε m /∂t in L 2 (Ω T ε ). To this end, we proceed as in [18] and consider the restriction operator…”

Section: Lemma 1 There Exists a Bounded Linear Operator Ementioning

confidence: 99%

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Homogenization of Smoluchowski Equations in Thin Heterogeneous Porous Domains

Noucheun,

Woukeng

2023

Mathematics

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In a thin heterogeneous porous layer, we carry out a multiscale analysis of Smoluchowski’s discrete diffusion–coagulation equations describing the evolution density of diffusing particles that are subject to coagulation in pairs. Assuming that the thin heterogeneous layer is made up of microstructures that are uniformly distributed inside, we obtain in the limit an upscaled model in the lower space dimension. We also prove a corrector-type result very useful in numerical computations. In view of the thin structure of the domain, we appeal to a concept of two-scale convergence adapted to thin heterogeneous media to achieve our goal.

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“…), no scaling is needed in the left-hand side of (18). Now, for (15), we follow exactly the same lines of reasoning as in [2] to obtain it.…”

Section: Well Posedness and Uniform Estimatesmentioning

confidence: 96%

“…Therefore, by integrating ( 19) over (0, t) (t ∈ (0, T]) and taking into account (18) and ( 20), we are led to…”

Section: Well Posedness and Uniform Estimatesmentioning

confidence: 99%

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Homogenization of Smoluchowski Equations in Thin Heterogeneous Porous Domains

Noucheun,

Woukeng

2023

Mathematics

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“…Therefore, later it turned out that it is even easier to prove the twoscale convergence of solutions of the problems to the solution of some homogenized two-scale problems. This approach is used, for example, in [10,13,14,17].…”

Section: Introductionmentioning

confidence: 99%

“…Numerical methods for such two-scale (micro-macro) models are discussed, for example, in [11,12,15]. Further details on the approaches and relevant references can be found in [10,12,14].…”

Section: Introductionmentioning

confidence: 99%

Homogenized Models with Memory Effect for Heterogeneous Periodic Media

Sandrakov

Семенов

2022

JODEA

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The homogenization of initial boundary value problems for heat conduction equations with asymptotically degenerate rapidly oscillating periodic coefficients are considered. Such problems model thermal processes in heterogeneous periodic media. Homogenized problems (whose solutions determine approximate asymptotics for solutions of the original problems) are presented. Estimates for the accuracy of the asymptotics and relevant convergence theorem are discussed. The homogenized problems have the form of initial boundary value problems for integro-differential equations in convolutions. The presence of convolutions in models for media is called the memory effect. Statements about the solvability and regularity for the problems and the homogenized problems are proved. These results are optimal even in the case of zero convolutions, when the homogenized problems coincide with the classical heat conduction problems.

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Homogenization of a nonlinear reaction‐diffusion problem in a perforated domain with different size obstacles

Ma,

Tang

2024

Z Angew Math Mech

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In this paper we consider a nonlinear reaction‐diffusion problem with low diffusion scales of order in a porous domain which periodically perforated by two different size obstacles. A nonlinear Neumann condition is prescribed on the boundaries of smaller obstacles, while a homogeneous Neumann condition is imposed on the other boundaries. Our aim is to derive the homogenized model as the small parameters tend to zero by using the method of three‐scale convergence and periodic reiterated unfolding operator. The final homogenized macroscopic model depends on three scales.

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Homogenization of Richards' equations in multiscale porous media with soft inclusions

Cited by 7 publications

References 34 publications

Homogenization of Smoluchowski Equations in Thin Heterogeneous Porous Domains

Homogenization of Smoluchowski Equations in Thin Heterogeneous Porous Domains

Homogenized Models with Memory Effect for Heterogeneous Periodic Media

Homogenization of a nonlinear reaction‐diffusion problem in a perforated domain with different size obstacles

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