logo AFST
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.
@article{AFST_2003_6_12_4_415_0,
     author = {Allaire, Gr\'egoire},
     title = {Dispersive limits in the homogenization of the wave equation},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 12},
     number = {4},
     year = {2003},
     pages = {415-431},
     doi = {10.5802/afst.1055},
     zbl = {1070.35006},
     mrnumber = {2060593},
     language = {en},
     url = {afst.centre-mersenne.org/item/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. doi : 10.5802/afst.1055. https://afst.centre-mersenne.org/item/AFST_2003_6_12_4_415_0/

[1] Allaire (G. ), Homogenization and two-scale convergence , SIAM J. Math. Anal. 23(6), p. 1482-1518 (1992). | MR 1185639 | Zbl 0770.35005

[2] Allaire (G. ), Capdeboscq (Y.), Homogenization of a spectral problem in neutronic multigroup diffusion, Comput. Methods Appl. Mech. Engrg. 187, p. 91-117 (2000). | MR 1765549 | Zbl 01501144

[3] Allaire (G. ), Malige (F.), Analyse asymptotique spectrale d'un problème de diffusion neutronique, C. R. Acad. Sci. Paris Série I 324, p. 939-944 (1997). | MR 1450451 | Zbl 0879.35153

[4] Allaire (G. ), Piatnitski (A.), Uniform Spectral Asymptotics for Singularly Perturbed Locally Periodic Operators, Com. in PDE 27, p. 705-725 (2002). | MR 1900560 | Zbl 1026.35012

[5] Bensoussan ( A. ), Lions (J.-L.), Papanicolaou (G.), Asymptotic analysis for periodic structures, North-Holland, Amsterdam, 1978. | MR 503330 | Zbl 0404.35001

[6] Brahim-Otsmane ( S.), Francfort (G.), Murat (F.), Correctors for the homogenization of the wave and heat equations, J. Math. Pures Appl. (9) 71, p. 197-231 (1992). | MR 1172450 | Zbl 0837.35016

[7] Castro ( C. ) , Zuazua ( E.), Low frequency asymptotic analysis of a string with rapidly oscillating density, SIAM J. Appl. Math. 60(4), p. 1205-1233 (2000 ). | MR 1760033 | Zbl 0967.34074

[8] Francfort ( G. ), Murat (F.), Oscillations and energy densities in the wave equation, Comm. Partial Differential Equations 17, p. 1785-1865 (1992). | MR 1194741 | Zbl 0803.35010

[9] Gérard (P. ), Microlocal defect measures, Comm. Partial Diff. Equations 16, p. 1761-1794 (1991 ). | MR 1135919 | Zbl 0770.35001

[10] Kozlov (S. ), Reducibility of quasiperiodic differential operators and averaging, Transc. Moscow Math. Soc., 2, p. 101-126 (1984). | Zbl 0566.35036

[11] Lions J.-L. , Contrôlabilité exacte, perturbations et stabilisation des systèmes distribués , Masson, Paris ( 1988).

[12] Nguetseng ( G.), A general convergence result for a functional related to the theory of homogenization, SIAM J. Math. Anal. 20(3), p. 608-623 (1989). | MR 990867 | Zbl 0688.35007

[13] Orive (R. ), Zuazua (E.), Pazoto (A.), Asymptotic expansion for damped wave equations with periodic coefficients, Math. Mod. Meth. Appl. Sci. 11, p. 1285-1310 (2001 ). | MR 1848202 | Zbl 1013.35014

[14] Sanchez-Palencia ( E.), Non homogeneous media and vibration theory , Lecture notes in physics 127, Springer Verlag (1980 ). | Zbl 0432.70002

[15] Tartar (L. ), 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). | MR 1069518 | Zbl 0774.35008

[16] Vanninathan ( M.), Homogenization of eigenvalue problems in perforated domains, Proc. Indian Acad. Sci. Math. Sci. 90, p. 239-271 (1981). | MR 635561 | Zbl 0486.35063