Free Access
Issue
ESAIM: COCV
Volume 11, Number 4, October 2005
Page(s) 542 - 573
DOI https://doi.org/10.1051/cocv:2005018
Published online 15 September 2005
  1. G. Allaire, Homogenization and two scale convergence. SIAM J. Math. Anal. 23 (1992) 1482–1518. [CrossRef] [MathSciNet] [Google Scholar]
  2. G. Allaire and C. Conca, Bloch wave homogenization for a spectral problem in fluid-solid structures. Arch. Rational Mech. Anal. 135 (1996) 197–257. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  3. G. Allaire and C. Conca, Boundary layers in the homogenization of a spectral problem in fluid-solid structures. SIAM J. Math. Anal. 29 (1997) 343–379. [CrossRef] [MathSciNet] [Google Scholar]
  4. A. Bensoussan, J.L. Lions and G. Papanicolaou, Asymptotic analysis for periodic structures. North Holland, Amsterdam (1978). [Google Scholar]
  5. C. Conca, S. Natesan and M. Vanninathan, Numerical solution of elliptic partial differential equations by Bloch waves method, XVII CEDYA: Congress on differential equations and applications/VII CMA: Congress on applied mathematics, Dep. Mat. Appl., Univ. Salamanca, Salamanca (2001) 63–83. [Google Scholar]
  6. C. Conca, R. Orive and M. Vanninathan, Bloch approximation in homogenization and applications. SIAM J. Math. Anal. 33 (2002) 1166–1198. [CrossRef] [MathSciNet] [Google Scholar]
  7. C. Conca, J. Planchard and M. Vanninathan, Fluids and periodic structures. John Wiley & Sons, New York, and Masson, Paris (1995). [Google Scholar]
  8. C. Conca and M. Vanninathan, Homogenization of periodic structures via Bloch decomposition. SIAM J. Appl. Math. 57 (1997) 1639–1659. [CrossRef] [MathSciNet] [Google Scholar]
  9. C. Conca and M. Vanninathan, Fourier approach to homogenization. ESAIM: COCV 8 (2002) 489–511. [CrossRef] [EDP Sciences] [Google Scholar]
  10. A.P. Cracknell and K.C. Wong, The Fermi surface. Clarendon press, Oxford (1973). [Google Scholar]
  11. G. Dal maso, An introduction to Γ-convergence. Birkhäuser, Boston (1993). [Google Scholar]
  12. P. Gérard, Microlocal defect measures. Commun. PDE 16 (1991) 1761–1794. [CrossRef] [Google Scholar]
  13. P. Gérard, P.A. Markowich, N.J. Mauser and F. Poupaud, Homogenization limits and Wigner transforms. Comm. Pure Appl. Math. 50 (1997) 323–379. [CrossRef] [MathSciNet] [Google Scholar]
  14. V.V. Jikov, S.M. Kozlov and O.A. Oleinik, Homogenization of Differential operators and Integral functionals. Berlin, Springer-Verlag (1994). [Google Scholar]
  15. T. Kato, Perturbation theory for linear operators. 2nd edition, Springer-Verlag, Berlin (1980). [Google Scholar]
  16. F. Murat and L. Tartar, H-Convergence, Topics in the Mathematical Modeling of Composite Materials, A. Charkaev and R. Kohn Eds. PNLDE 31, Birkhäuser, Boston (1997). [Google Scholar]
  17. G. Nguetseng, A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal. 20 (1989) 608–623. [CrossRef] [MathSciNet] [Google Scholar]
  18. O.A. Oleinik, A.S. Shamaev and G.A. Yosifian, Mathematical problems in elasticity and homogenization. North Holland, Amsterdam (1992). [Google Scholar]
  19. F. Rellich, Perturbation theory of eigenvalue problems. Gordon and Breach science publishers, New York (1969). [Google Scholar]
  20. M. Roseau, Vibrations in Mechanical systems: Analytical methods and applications. Springer-Verlag, Berlin (1987). [Google Scholar]
  21. W. Rudin, Functional analysis. 2nd edition, Mc-Graw Hill, New York (1991). [Google Scholar]
  22. J. Sínchez-Hubert and E. Sínchez-Palencia, Vibration and coupling of continuous systems: asymptotic methods. Springer-Verlag, Berlin (1989). [Google Scholar]
  23. E. Sínchez-Palencia, Non-homogeneous media and vibration theory. Lect. Notes Phys. 127 (1980). [Google Scholar]
  24. F. Santosa and W.W. Symes, A dispersive effective medium for wave propagation in periodic composites. SIAM J. Appl. Math. 51 (1991) 984–1005. [CrossRef] [MathSciNet] [Google Scholar]
  25. S. Sivaji Ganesh and M. Vanninathan, Bloch wave homogenization of scalar elliptic operators. Asymptotic Analysis 39 (2004) 15–44. [MathSciNet] [Google Scholar]
  26. L. Tartar, H-measures, a new approach for studying homogenization, oscillations and concentration effects in partial differential equations. Proc. Roy. Soc. Edin. Sect. A 115 (1990) 193–230. [Google Scholar]
  27. N. Turbé, Applications of Bloch decomposition to periodic elastic and viscoelastic media. Math. Meth. Appl. Sci. 4 (1982) 433–449. [CrossRef] [Google Scholar]

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