Dispersive limits in the homogenization of the wave equation

Grégoire Allaire

Annales de la Faculté des sciences de Toulouse : Mathématiques (2003)

  • Volume: 12, Issue: 4, page 415-431
  • ISSN: 0240-2963

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Allaire, Grégoire. "Dispersive limits in the homogenization of the wave equation." Annales de la Faculté des sciences de Toulouse : Mathématiques 12.4 (2003): 415-431. <http://eudml.org/doc/73610>.

@article{Allaire2003,
author = {Allaire, Grégoire},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {homogenized problem; Klein-Gordon equation; periodic medium},
language = {eng},
number = {4},
pages = {415-431},
publisher = {Université Paul Sabatier, Institut de Mathématiques},
title = {Dispersive limits in the homogenization of the wave equation},
url = {http://eudml.org/doc/73610},
volume = {12},
year = {2003},
}

TY - JOUR
AU - Allaire, Grégoire
TI - Dispersive limits in the homogenization of the wave equation
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 2003
PB - Université Paul Sabatier, Institut de Mathématiques
VL - 12
IS - 4
SP - 415
EP - 431
LA - eng
KW - homogenized problem; Klein-Gordon equation; periodic medium
UR - http://eudml.org/doc/73610
ER -

References

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  3. [3] Allaire ( G. ), Malige ( F.), Analyse asymptotique spectrale d'un problème de diffusion neutronique, C. R. Acad. Sci. Paris SérieI324, p. 939-944 (1997). Zbl0879.35153MR1450451
  4. [4] Allaire ( G. ), Piatnitski ( A.), Uniform Spectral Asymptotics for Singularly Perturbed Locally Periodic Operators, Com. in PDE27, p. 705-725 (2002). Zbl1026.35012MR1900560
  5. [5] Bensoussan ( A. ), Lions ( J.-L.), Papanicolaou ( G.), Asymptotic analysis for periodic structures, North-Holland, Amsterdam, 1978. Zbl0404.35001MR503330
  6. [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). Zbl0837.35016MR1172450
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  8. [8] Francfort ( G. ), Murat ( F.), Oscillations and energy densities in the wave equation, Comm. Partial Differential Equations17, p. 1785-1865 (1992). Zbl0803.35010MR1194741
  9. [9] Gérard ( P. ), Microlocal defect measures, Comm. Partial Diff. Equations16, p. 1761-1794 (1991 ). Zbl0770.35001MR1135919
  10. [10] Kozlov ( S. ), Reducibility of quasiperiodic differential operators and averaging, Transc. Moscow Math. Soc., 2, p. 101-126 (1984). Zbl0566.35036
  11. [11] Lions J.-L. , Contrôlabilité exacte, perturbations et stabilisation des systèmes distribués , Masson, Paris ( 1988). Zbl0653.93002
  12. [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). Zbl0688.35007MR990867
  13. [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 ). Zbl1013.35014MR1848202
  14. [14] Sanchez-Palencia ( E.), Non homogeneous media and vibration theory , Lecture notes in physics127, Springer Verlag (1980 ). Zbl0432.70002
  15. [15] Tartar ( L. ), H-measures, a new approach for studying homogenization, oscillations and concentration effects in partial differential equations, Proc. Roy. Soc. Edinburgh115A, p. 193-230 (1990). Zbl0774.35008MR1069518
  16. [16] Vanninathan ( M.), Homogenization of eigenvalue problems in perforated domains, Proc. Indian Acad. Sci. Math. Sci.90, p. 239-271 (1981). Zbl0486.35063MR635561

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