ESAIM: Control, Optimisation and Calculus of Variations (ESAIM: COCV)

Trends in Nonlinear Analysis

Andro Mikelić
Trends in Nonlinear Analysis 225 (2003)
DOI: 10.1007/978-3-662-05281-5_5
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Moment bounds on the corrector of stochastic homogenization of non-symmetric elliptic finite difference equations

Jonathan Ben-Artzi, Daniel Marahrens and Stefan Neukamm
Communications in Partial Differential Equations 42 (2) 179 (2017)
DOI: 10.1080/03605302.2017.1281298
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Multiscale and Multiresolution Methods

Christoph Schwab and Ana-Maria Matache
Lecture Notes in Computational Science and Engineering, Multiscale and Multiresolution Methods 20 197 (2002)
DOI: 10.1007/978-3-642-56205-1_4
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Homogenization of parabolic equation in an evolving domain with an oscillating boundary

T. Muthukumar, Jean-Pierre Raymond and K. Sankar
Journal of Mathematical Analysis and Applications 463 (2) 838 (2018)
DOI: 10.1016/j.jmaa.2018.03.063
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Asymptotic analysis and error estimates for an optimal control problem with oscillating boundaries

A. K. Nandakumaran, Ravi Prakash and J.-P. Raymond
ANNALI DELL'UNIVERSITA' DI FERRARA 58 (1) 143 (2012)
DOI: 10.1007/s11565-011-0135-3
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Boundary effects on effective conductivity of random heterogeneous media with spherical inclusions

A. Rabinovich, G. Dagan and T. Miloh
Physical Review E 86 (4) (2012)
DOI: 10.1103/PhysRevE.86.046601
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Test high volume of citations

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Testing new deposit code 4 (2) 28 (2012)
DOI: 10.5555/20120925-a1
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Third-Order Corrections in Periodic Homogenization for Elliptic Problem

Tebib Hawa and Chacha Djamal Ahmed
Mediterranean Journal of Mathematics 18 (4) (2021)
DOI: 10.1007/s00009-021-01727-3
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Scattering by a Bounded Highly Oscillating Periodic Medium and the Effect of Boundary Correctors

Fioralba Cakoni, Bojan B. Guzina, Shari Moskow and Tayler Pangburn
SIAM Journal on Applied Mathematics 79 (4) 1448 (2019)
DOI: 10.1137/19M1237089
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DISPERSIVE EFFECTIVE MODELS FOR WAVES IN HETEROGENEOUS MEDIA

AGNES LAMACZ
Mathematical Models and Methods in Applied Sciences 21 (09) 1871 (2011)
DOI: 10.1142/S021820251100557X
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An optimal quantitative two-scale expansion in stochastic homogenization of discrete elliptic equations

Antoine Gloria, Stefan Neukamm and Felix Otto
ESAIM: Mathematical Modelling and Numerical Analysis 48 (2) 325 (2014)
DOI: 10.1051/m2an/2013110
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Asymptotic Homogenization of Composite Materials and Structures

Alexander L. Kalamkarov, Igor V. Andrianov and Vladyslav V. Danishevs’kyy
Applied Mechanics Reviews 62 (3) 030802 (2009)
DOI: 10.1115/1.3090830
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Scattering by a highly oscillating surface

A. Bendali and J.-R. Poirier
Mathematical Methods in the Applied Sciences 38 (13) 2785 (2015)
DOI: 10.1002/mma.3261
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Multiscale Asymptotic Analysis and Computation of Optimal Control for Elliptic Systems with Constraints

Jianjun Liu, Liqun Cao and Ningning Yan
SIAM Journal on Numerical Analysis 51 (4) 1978 (2013)
DOI: 10.1137/120869614
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Multiscale Finite Element approach for “weakly” random problems and related issues

Claude Le Bris, Frédéric Legoll and Florian Thomines
ESAIM: Mathematical Modelling and Numerical Analysis 48 (3) 815 (2014)
DOI: 10.1051/m2an/2013122
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Effective slip law for general viscous flows over an oscillating surface

Andro Mikelić, Šárka Nečasová and Maria Neuss-Radu
Mathematical Methods in the Applied Sciences n/a (2013)
DOI: 10.1002/mma.2923
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Effective boundary condition for Stokes flow over a very rough surface

Youcef Amirat, Olivier Bodart, Umberto De Maio and Antonio Gaudiello
Journal of Differential Equations 254 (8) 3395 (2013)
DOI: 10.1016/j.jde.2013.01.024
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Upscaling of reactive flows in domains with moving oscillating boundaries

Iuliu Sorin Pop, Tycho van Noorden and Kundan Kumar
Discrete and Continuous Dynamical Systems - Series S 7 (1) 95 (2013)
DOI: 10.3934/dcdss.2014.7.95
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The boundary behavior of a composite material

Maria Neuss-Radu
ESAIM: Mathematical Modelling and Numerical Analysis 35 (3) 407 (2001)
DOI: 10.1051/m2an:2001122
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Rigorous upscaling of rough boundaries for reactive flows

K. Kumar, M. van Helvoort and I.S. Pop
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 94 (7-8) 623 (2014)
DOI: 10.1002/zamm.201200226
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Asymptotic Approximation of the Solution of the Laplace Equation in a Domain with Highly Oscillating Boundary

Y. Amirat, O. Bodart, U. De Maio and A. Gaudiello
SIAM Journal on Mathematical Analysis 35 (6) 1598 (2004)
DOI: 10.1137/S0036141003414877
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Second order corrector in the homogenization of a conductive-radiative heat transfer problem

Zakaria Habibi and Grégoire Allaire
Discrete and Continuous Dynamical Systems - Series B 18 (1) 1 (2012)
DOI: 10.3934/dcdsb.2013.18.1
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Modeling of thermophysical properties in heterogeneous periodic media according to a multi-scale approach: Effective conductivity tensor and edge effects

A. Matine, N. Boyard, P. Cartraud, G. Legrain and Y. Jarny
International Journal of Heat and Mass Transfer 62 586 (2013)
DOI: 10.1016/j.ijheatmasstransfer.2013.03.036
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Asymptotic analysis of second-order boundary layer correctors

Daniel Onofrei and Bogdan Vernescu
Applicable Analysis 91 (6) 1097 (2012)
DOI: 10.1080/00036811.2011.616498
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Second-order two-scale method for bending behavior analysis of composite plate with 3-D periodic configuration and its approximation

ZiQiang Wang and JunZhi Cui
Science China Mathematics 57 (8) 1713 (2014)
DOI: 10.1007/s11425-014-4831-1
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Calculation of Thermoelastic Stresses in a Joint Formed in Explosion Welding

A. G. Kolpakov and S. I. Rakin
Journal of Applied Mechanics and Technical Physics 61 (2) 277 (2020)
DOI: 10.1134/S0021894420020145
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Inertia and Roughness-Induced Effects on the Porous Medium Flow Through a Corrugated Channel

Eduard Marušić-Paloka and Igor Pažanin
Transport in Porous Media 134 (3) 621 (2020)
DOI: 10.1007/s11242-020-01460-7
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Effective Fluid Behavior in Domain with Rough Boundary and the Darcy--Weisbach Law

Eduard Marušić-Paloka
SIAM Journal on Applied Mathematics 79 (4) 1244 (2019)
DOI: 10.1137/18M1183376
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Liouville Principles and a Large-Scale Regularity Theory for Random Elliptic Operators on the Half-Space

Julian Fischer and Claudia Raithel
SIAM Journal on Mathematical Analysis 49 (1) 82 (2017)
DOI: 10.1137/16M1070384
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Two-scale homogenization of the Poisson equation with friction boundary condition in a perforated domain

L. Baffico
Asymptotic Analysis 96 (3-4) 331 (2016)
DOI: 10.3233/ASY-151346
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Multiscale Approach for Optimal Design in Conductivity of Composite Materials

Jianjun Liu, Liqun Cao, Ningning Yan and Junzhi Cui
SIAM Journal on Numerical Analysis 53 (3) 1325 (2015)
DOI: 10.1137/13094904X
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Stokes’ System in a Domain with Oscillating Boundary: Homogenization and Error Analysis of an Interior Optimal Control Problem

A. K. Nandakumaran, Ravi Prakash and J.-P. Raymond
Numerical Functional Analysis and Optimization 35 (3) 323 (2014)
DOI: 10.1080/01630563.2013.812657
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Homogenization of Highly Oscillating Boundaries with Strongly Contrasting Diffusivity

Antonio Gaudiello and Ali Sili
SIAM Journal on Mathematical Analysis 47 (3) 1671 (2015)
DOI: 10.1137/140987225
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Effective laws for the Poisson equation on domains with curved oscillating boundaries

N. Neuss, M. Neuss-Radu and A. Mikelić
Applicable Analysis 85 (5) 479 (2006)
DOI: 10.1080/00036810500340476
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Applications of Fourier Analysis in Homogenization of Dirichlet Problem III: Polygonal Domains

Hayk Aleksanyan, Henrik Shahgholian and Per Sjölin
Journal of Fourier Analysis and Applications 20 (3) 524 (2014)
DOI: 10.1007/s00041-014-9327-4
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On multiscale homogenization problems in boundary layer theory

Youcef Amirat, Gregory A. Chechkin and Maxim Romanov
Zeitschrift für angewandte Mathematik und Physik 63 (3) 475 (2012)
DOI: 10.1007/s00033-011-0167-7
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Localization for the Schrödinger Equation in a Locally Periodic Medium

Grégoire Allaire and Mariapia Palombaro
SIAM Journal on Mathematical Analysis 38 (1) 127 (2006)
DOI: 10.1137/050635572
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Homogenization of a Nonlinear Elliptic Boundary Value Problem Modeling Galvanic Currents

Y. S. Bhat and S. Moskow
Multiscale Modeling & Simulation 5 (1) 149 (2006)
DOI: 10.1137/050637042
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Homogenization of a Conductive and Radiative Heat Transfer Problem

Grégoire Allaire and Karima El Ganaoui
Multiscale Modeling & Simulation 7 (3) 1148 (2009)
DOI: 10.1137/080714737
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First-Order Corrector for the Homogenization of the Criticality Eigenvalue Problem in the Even Parity Formulation of the Neutron Transport

Guillaume Bal
SIAM Journal on Mathematical Analysis 30 (6) 1208 (1999)
DOI: 10.1137/S0036141098338855
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A Multiscale Finite Element Method for Oscillating Neumann Problem on Rough Domain

Pingbing Ming and Xianmin Xu
Multiscale Modeling & Simulation 14 (4) 1276 (2016)
DOI: 10.1137/15M1044709
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Convergence Analysis for The Numerical Boundary Corrector for Elliptic Equations with Rapidly Oscillating Coefficients

Marcus Sarkis and Henrique Versieux
SIAM Journal on Numerical Analysis 46 (2) 545 (2008)
DOI: 10.1137/060654773
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Periodic Controls in an Oscillating Domain: Controls via Unfolding and Homogenization

A. K. Nandakumaran, Ravi Prakash and Bidhan Chandra Sardar
SIAM Journal on Control and Optimization 53 (5) 3245 (2015)
DOI: 10.1137/140994575
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Applications of Fourier analysis in homogenization of Dirichlet problem I. Pointwise estimates

Hayk Aleksanyan, Henrik Shahgholian and Per Sjölin
Journal of Differential Equations 254 (6) 2626 (2013)
DOI: 10.1016/j.jde.2012.12.017
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On the Homogenization of a Scalar Scattering Problem for Highly Oscillating Anisotropic Media

Fioralba Cakoni, Bojan B. Guzina and Shari Moskow
SIAM Journal on Mathematical Analysis 48 (4) 2532 (2016)
DOI: 10.1137/15M1018009
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Generation of Optimal Periodic Oscillations for the Control of Boundary Layers

Abderrahmane Habbal
SIAM Journal on Control and Optimization 41 (3) 712 (2002)
DOI: 10.1137/S0363012999354892
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Slow Convergence in Periodic Homogenization Problems for Divergence-Type Elliptic Operators

Hayk Aleksanyan
SIAM Journal on Mathematical Analysis 48 (5) 3345 (2016)
DOI: 10.1137/15M1040165
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Scattering, Homogenization, and Interface Effects for Oscillatory Potentials with Strong Singularities

Vincent Duchêne and Michael I. Weinstein
Multiscale Modeling & Simulation 9 (3) 1017 (2011)
DOI: 10.1137/100811672
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Periodic Homogenization of Green and Neumann Functions

Carlos Kenig, Fanghua Lin and Zhongwei Shen
Communications on Pure and Applied Mathematics 67 (8) 1219 (2014)
DOI: 10.1002/cpa.21482
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Homogenization of highly oscillating boundaries and reduction of dimension for a monotone problem

Dominique Blanchard and Antonio Gaudiello
ESAIM: Control, Optimisation and Calculus of Variations 9 449 (2003)
DOI: 10.1051/cocv:2003022
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Asymptotic Analysis of Boundary Layer Correctors in Periodic Homogenization

Christophe Prange
SIAM Journal on Mathematical Analysis 45 (1) 345 (2013)
DOI: 10.1137/120876502
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Thermal properties of composite materials :effective conductivity tensor and edge effects

A Matine, N Boyard, P Cartraud, G Legrain and Y Jarny
Journal of Physics: Conference Series 395 012014 (2012)
DOI: 10.1088/1742-6596/395/1/012014
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Homogenization of the Brush Problem with a Source Term in L 1

Antonio Gaudiello, Olivier Guibé and François Murat
Archive for Rational Mechanics and Analysis 225 (1) 1 (2017)
DOI: 10.1007/s00205-017-1079-2
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Numerical approximation of laminar flows over rough walls with sharp asperities

Youcef Amirat and Olivier Bodart
Journal of Computational and Applied Mathematics 164-165 25 (2004)
DOI: 10.1016/S0377-0427(03)00639-3
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Two-scale analysis for very rough thin layers. An explicit characterization of the polarization tensor

Ionel Sorin Ciuperca, Ronan Perrussel and Clair Poignard
Journal de Mathématiques Pures et Appliquées 95 (3) 277 (2011)
DOI: 10.1016/j.matpur.2010.12.001
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An asymptotic strategy to couple homogenized elastic structures

Alexander G. Kolpakov, Igor V. Andrianov, Sergei I. Rakin and Graham A. Rogerson
International Journal of Engineering Science 131 26 (2018)
DOI: 10.1016/j.ijengsci.2018.04.006
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Quantitative Analysis of Boundary Layers in Periodic Homogenization

Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat and Christophe Prange
Archive for Rational Mechanics and Analysis 226 (2) 695 (2017)
DOI: 10.1007/s00205-017-1142-z
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Boundary Layers in Periodic Homogenization of Neumann Problems

Zhongwei Shen and Jinping Zhuge
Communications on Pure and Applied Mathematics 71 (11) 2163 (2018)
DOI: 10.1002/cpa.21740
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On the best constant matrix approximating an oscillatory matrix-valued coefficient in divergence-form operators

Claude Le Bris, Frédéric Legoll and Simon Lemaire
ESAIM: Control, Optimisation and Calculus of Variations (2018)
DOI: 10.1051/cocv/2017061
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Functionally graded lattice structure topology optimization for the design of additive manufactured components with stress constraints

Lin Cheng, Jiaxi Bai and Albert C. To
Computer Methods in Applied Mechanics and Engineering 344 334 (2019)
DOI: 10.1016/j.cma.2018.10.010
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Cell Averaging Two-Scale Convergence: Applications to Periodic Homogenization

François Alouges and Giovanni Di Fratta
Multiscale Modeling & Simulation 15 (4) 1651 (2017)
DOI: 10.1137/16M1085309
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Homogenization of Elastic Dielectric Composites with Rapidly Oscillating Passive and Active Source Terms

Victor Lefèvre and Oscar Lopez-Pamies
SIAM Journal on Applied Mathematics 77 (6) 1962 (2017)
DOI: 10.1137/17M1110432
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A Mathematical and Numerical Framework for Bubble Meta-Screens

Habib Ammari, Brian Fitzpatrick, David Gontier, Hyundae Lee and Hai Zhang
SIAM Journal on Applied Mathematics 77 (5) 1827 (2017)
DOI: 10.1137/16M1090235
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Boundary layer effect at the edge of fibrous composites using homogenization theory

S. Koley, P.M. Mohite and C.S. Upadhyay
Composites Part B: Engineering 173 106815 (2019)
DOI: 10.1016/j.compositesb.2019.05.026
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Homogenization and boundary layers in domains of finite type

Jinping Zhuge
Communications in Partial Differential Equations 43 (4) 549 (2018)
DOI: 10.1080/03605302.2018.1446160
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Shallow layer correction for Spectral Element like methods

Y. Capdeville and J.-J. Marigo
Geophysical Journal International 172 (3) 1135 (2008)
DOI: 10.1111/j.1365-246X.2007.03703.x
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Asymptotic Expansions of Eigenelements of the Laplace Operator in a Domain with Many “Light” Concentrated Masses Closely Located on the Boundary. Multi-Dimensional Case

G. A. Chechkin
Journal of Mathematical Sciences 128 (5) 3263 (2005)
DOI: 10.1007/s10958-005-0268-y
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Boundary layers in fibrous composite materials

Igor V. Andrianov, Vladyslav V. Danishevs’kyy and Dieter Weichert
Acta Mechanica 216 (1-4) 3 (2011)
DOI: 10.1007/s00707-010-0333-6
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Asymptotics of simple eigenvalues and eigenfunctions for the Laplace operator in a domain with an oscillating boundary

Y. Amirat, G. A. Chechkin and R. R. Gadyl’shin
Computational Mathematics and Mathematical Physics 46 (1) 97 (2006)
DOI: 10.1134/S0965542506010118
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Multiscale Problems in Science and Technology

Maria Neuss-Radu
Multiscale Problems in Science and Technology 243 (2002)
DOI: 10.1007/978-3-642-56200-6_10
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Approximate transmission conditions through a rough thin layer: The case of periodic roughness

I. S. CIUPERCA, M. JAI and C. POIGNARD
European Journal of Applied Mathematics 21 (1) 51 (2010)
DOI: 10.1017/S095679250999012X
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Homogenization of an evolution problem with $$ L\log L$$ L log L data in a domain with oscillating boundary

Antonio Gaudiello and Olivier Guibé
Annali di Matematica Pura ed Applicata (1923 -) 197 (1) 153 (2018)
DOI: 10.1007/s10231-017-0673-0
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Diffractive behavior of the wave equation in periodic media: weak convergence analysis

Grégoire Allaire, Mariapia Palombaro and Jeffrey Rauch
Annali di Matematica Pura ed Applicata 188 (4) (2009)
DOI: 10.1007/s10231-008-0089-y
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Uniform estimate of an iterative method for elliptic problems with rapidly oscillating coefficients

Chenlin Gu
Stochastics and Partial Differential Equations: Analysis and Computations 8 (4) 787 (2020)
DOI: 10.1007/s40072-019-00159-1
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Modelling viscoelastic wave phenomenon by homogenisation of the poroelasticity equations

Q. LI, F. SANTOSA, B. WHEELOCK and K. GOVIL
European Journal of Applied Mathematics 32 (5) 846 (2021)
DOI: 10.1017/S0956792520000467
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Optimal Convergence Rates for Elliptic Homogenization Problems in Nondivergence-Form: Analysis and Numerical Illustrations

Timo Sprekeler and Hung V. Tran
Multiscale Modeling & Simulation 19 (3) 1453 (2021)
DOI: 10.1137/20M137121X
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Mathematical Analysis of Electromagnetic Plasmonic Metasurfaces

Habib Ammari, Bowen Li and Jun Zou
Multiscale Modeling & Simulation 18 (2) 758 (2020)
DOI: 10.1137/19M1275097
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Effects of boundary roughness and inertia on the fluid flow through a corrugated pipe and the formula for the Darcy–Weisbach friction coefficient

Eduard Marušić-Paloka and Igor Pažanin
International Journal of Engineering Science 152 103293 (2020)
DOI: 10.1016/j.ijengsci.2020.103293
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Limiting boundary correctors for periodic microstructures and inverse homogenization series

Fioralba Cakoni, Shari Moskow and Tayler Pangburn
Inverse Problems 36 (6) 065009 (2020)
DOI: 10.1088/1361-6420/ab8bc6
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Mathematical and numerical framework for metasurfaces using thin layers of periodically distributed plasmonic nanoparticles

Habib Ammari, Matias Ruiz, Wei Wu, Sanghyeon Yu and Hai Zhang
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472 (2193) 20160445 (2016)
DOI: 10.1098/rspa.2016.0445
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On a pore-scale stationary diffusion equation: Scaling effects and correctors for the homogenization limit

Vo Anh Khoa, Thi Kim Thoa Thieu and Ekeoma Rowland Ijioma
Discrete & Continuous Dynamical Systems - B 26 (5) 2451 (2021)
DOI: 10.3934/dcdsb.2020190
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Macroscale modelling of multilayer diffusion: Using volume averaging to correct the boundary conditions

E.J. Carr, I.W. Turner and P. Perré
Applied Mathematical Modelling 47 600 (2017)
DOI: 10.1016/j.apm.2017.03.044
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Periodic homogenization with an interface: The multi-dimensional case

Martin Hairer and Charles Manson
The Annals of Probability 39 (2) (2011)
DOI: 10.1214/10-AOP564
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Dynamical one-dimensional models of passive piezoelectric sensors

Cédric Bellis and Sébastien Imperiale
Mathematics and Mechanics of Solids 19 (5) 451 (2014)
DOI: 10.1177/1081286512469980
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Stress minimization for lattice structures. Part I: Micro-structure design

A. Ferrer, P. Geoffroy-Donders and G. Allaire
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 379 (2201) 20200109 (2021)
DOI: 10.1098/rsta.2020.0109
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High Order Homogenization of the Stokes System in a Periodic Porous Medium

Florian Feppon
SIAM Journal on Mathematical Analysis 53 (3) 2890 (2021)
DOI: 10.1137/20M1348078
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Igor V. Andrianov, Jan Awrejcewicz and Vladyslav V. Danishevskyy
77 1 (2018)
DOI: 10.1007/978-3-319-65786-8_1
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Nguyen Nhat Binh Trinh, Michel Lenczner, Frederic Zamkotsian and Nicolas Ratier
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DOI: 10.1109/EuroSimE.2018.8369936
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