@article{AFST_2003_6_12_4_415_0,
author = {Gr\'egoire Allaire},
title = {Dispersive limits in the homogenization of the wave equation},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {415--431},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 12},
number = {4},
year = {2003},
zbl = {1070.35006},
mrnumber = {2060593},
language = {en},
url = {https://afst.centre-mersenne.org/item/AFST_2003_6_12_4_415_0/}
}
TY - JOUR AU - Grégoire Allaire TI - Dispersive limits in the homogenization of the wave equation JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2003 SP - 415 EP - 431 VL - 12 IS - 4 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/item/AFST_2003_6_12_4_415_0/ LA - en ID - AFST_2003_6_12_4_415_0 ER -
%0 Journal Article %A Grégoire Allaire %T Dispersive limits in the homogenization of the wave equation %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2003 %P 415-431 %V 12 %N 4 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/item/AFST_2003_6_12_4_415_0/ %G en %F AFST_2003_6_12_4_415_0
Grégoire Allaire. Dispersive limits in the homogenization of the wave equation. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 12 (2003) no. 4, pp. 415-431. https://afst.centre-mersenne.org/item/AFST_2003_6_12_4_415_0/
[1] , Homogenization and two-scale convergence , SIAM J. Math. Anal. 23(6), p. 1482-1518 (1992). | Zbl | MR
[2] , , Homogenization of a spectral problem in neutronic multigroup diffusion, Comput. Methods Appl. Mech. Engrg. 187, p. 91-117 (2000). | Zbl | MR
[3] , , Analyse asymptotique spectrale d'un problème de diffusion neutronique, C. R. Acad. Sci. Paris Série I 324, p. 939-944 (1997). | Zbl | MR
[4] , , Uniform Spectral Asymptotics for Singularly Perturbed Locally Periodic Operators, Com. in PDE 27, p. 705-725 (2002). | Zbl | MR
[5] , , , Asymptotic analysis for periodic structures, North-Holland, Amsterdam, 1978. | Zbl | MR
[6] , , , Correctors for the homogenization of the wave and heat equations, J. Math. Pures Appl. (9) 71, p. 197-231 (1992). | Zbl | MR
[7] , , Low frequency asymptotic analysis of a string with rapidly oscillating density, SIAM J. Appl. Math. 60(4), p. 1205-1233 (2000 ). | Zbl | MR
[8] , , Oscillations and energy densities in the wave equation, Comm. Partial Differential Equations 17, p. 1785-1865 (1992). | Zbl | MR
[9] , Microlocal defect measures, Comm. Partial Diff. Equations 16, p. 1761-1794 (1991 ). | Zbl | MR
[10] , Reducibility of quasiperiodic differential operators and averaging, Transc. Moscow Math. Soc., 2, p. 101-126 (1984). | Zbl
[11] , Contrôlabilité exacte, perturbations et stabilisation des systèmes distribués , Masson, Paris ( 1988).
[12] , A general convergence result for a functional related to the theory of homogenization, SIAM J. Math. Anal. 20(3), p. 608-623 (1989). | Zbl | MR
[13] , , , Asymptotic expansion for damped wave equations with periodic coefficients, Math. Mod. Meth. Appl. Sci. 11, p. 1285-1310 (2001 ). | Zbl | MR
[14] , Non homogeneous media and vibration theory , Lecture notes in physics 127, Springer Verlag (1980 ). | Zbl
[15] , H-measures, a new approach for studying homogenization, oscillations and concentration effects in partial differential equations, Proc. Roy. Soc. Edinburgh 115A, p. 193-230 (1990). | Zbl | MR
[16] , Homogenization of eigenvalue problems in perforated domains, Proc. Indian Acad. Sci. Math. Sci. 90, p. 239-271 (1981). | Zbl | MR