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Periodic unfolding and homogenization. (English. Abridged French version) Zbl 1001.49016
Summary: A novel approach to periodic homogenization is proposed, based on an unfolding method, which leads to a fixed domain problem (without singularly oscillating coefficients). This method is elementary in nature and applies to cases of periodic multi-scale problems in domains with or without holes (including truss-like structures).

49J45 Methods involving semicontinuity and convergence; relaxation
74Q10 Homogenization and oscillations in dynamical problems of solid mechanics
Full Text: DOI
[1] Allaire, G., Homogenization and two-scale convergence, SIAM J. math. anal., 23, 1482-1518, (1992) · Zbl 0770.35005
[2] Allaire, G.; Briane, M., Multiscale convergence and reiterated homogenization, Proc. roy. soc. Edinburgh sect. A, 126, 297-342, (1996) · Zbl 0866.35017
[3] Arbogast, T.; Douglas, J.; Hornung, U., Derivation of the double porosity model of single phase flow via homogenization theory, SIAM J. math. anal., 21, 823-836, (1990) · Zbl 0698.76106
[4] Casado-Díaz, J., Two-scale convergence for nonlinear Dirichlet problems in perforated domains, Proc. roy. soc. Edinburgh, sect. A, 130, 249-276, (2000) · Zbl 0977.35019
[5] Casado-Díaz, J.; Luna-Laynez, M.; Martı́n, J.D., An adaptation of the multi-scale methods for the analysis of bery thin reticulated structures, C. R. acad. sci. Paris, Série I, 332, 223-228, (2001) · Zbl 0984.35017
[6] J. Casado-Dı́az, M. Luna-Laynez, J.D. Martı́n, Homogenization of nonhomogeneous monotone operators in thin reticulated structures: a multi-scale method, to appear
[7] Cioranescu, D.; Donato, P., An introduction to homogenization, Oxford lecture series in math. appl., 17, (1999), Oxford University Press
[8] A. Ene, J. Saint Jean Paulin, On a model of fractured porous media, Publication Dép. Math. Université de Metz 2 (1996)
[9] Defranceschi, A.; Dal Maso, G., Correctors for the homogenization of monotone operators, Differential integral equations, 3, 6, 1151-1166, (1990) · Zbl 0733.35005
[10] G. Griso, Analyse asymptotique de structures réticulées. Thèse Université Pierre et Marie Curie (Paris VI), 1996
[11] Griso, G., Thin reticulated structures, (), 161-182 · Zbl 0845.35009
[12] Nguetseng, G., A general convergence result for a functional related to the theory of homogenization, SIAM J. math. anal., 20, 608-629, (1989) · Zbl 0688.35007
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