An introduction to homogenization

By Doina Cioranescu, Patrizia Donato. 2000

1,440 citations recorded by the source corpus.

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Citations in the corpus

Asymptotic and numerical homogenization (2008, methodology): “We refer, for example, to the recent texts by Jikov, Kozlov and Oleinik (1991), Allaire et al. (1993), Cioranescu and Donato (2000), Marchenko and Khruslov (2006) and Pavliotis and Stewart (2007).”
Two-scale convergence of some integral functionals (2007, unknown): “the monographs [6,11,15,27,29,35,38,50] and their bibliographies.”
Homogenization in polygonal domains (2011, background): “It has given birth to a rich mathematical theory (see the articles [14, 19] and textbooks [11, 8], among many).”
Reiterated homogenization of monotone operators (2000, background): “This definition is a variant of the one introduced in [2] for the casep= 2 (seealso [1,5] and [7]).”
Homogenization and behaviour of optimal controls for the wave equation in domains with oscillating boundary (2007, methodology): “to [ CD1 ] , [CDMZ 3], [CS] for homogenization of hyperbolic equations, to [L4], [L5] for optimal control and [CDMZ 1], [CDMZ 2] for related problems.”
Microstructures to control elasticity in 3D printing (2015, methodology): “…homogenization theory was developed to efficiently simulate inhomogeneous materials with fine structures, allowing microscopic behavior to be averaged into a coarser macroscopic representation with equivalent behavior at the macroscopic scale [Michel et al. 1999; Cioranescu and Donato 2000].”
Homogenization and boundary layers (2012, background): “We refer to the reknown book [7] for a good overview (see also the more recent books [17, 10, 9, 22]).”
Stochastic homogenization of Hamilton‐Jacobi‐Bellman equations (2006, background): “There is a vast literature on periodic and quasi-periodic homogenization of linear and nonlinear partial differential equations (see, for example, monographs [1, 2, 5, 7, 10, 15] and references therein).”
Sulfate attack in sewer pipes: Derivation of a concrete corrosion model via two-scale convergence (2010, background): “, [6,7,8], while a few relevant (remotely resembling) worked-out examples of this averaging methodology are explained, for instance, in [9,10,11,12,13,14].”
Homogenization of diffusion problems with a nonlinear interfacial resistance (2015, background): “It gives an elementary proof for the classical periodic homogenization problem originally considered in [6] (see also [14,40]) and corrector results under natural assumptions (see [12] for a comprehensive presentation).”
The Periodic Unfolding Method in Homogenization (2008, background): “Section 6 is devoted to a corrector result, which holds without any additional regularity on the data (contrary to all previous proofs; see [11], [30], and [59]).”
Quantitative Stochastic Homogenization and Large-Scale Regularity (2017, background): “There is a vast and rich mathematical literature on homogenization developed in the last forty years and already many good expositions on the topic (see for instance the books [5, 22, 27, 33, 34, 74, 80, 105, 113]).”
Towards a two-scale calculus (2006, unknown): “[3, 7, 16, 19, 24, 28–31].”
Optimal Local Multi-scale Basis Functions for Linear Elliptic Equations with Rough Coefficient (2015, unknown): “Consider a set of basis functions”
Finite difference heterogeneous multi-scale method for homogenization problems (2003, background): “These analytical techniques have been studied for many years (see for example [5,6], and the references therein).”