Homogenization limits of diffusion equations in thin domains

Alain Damlamian; Michael Vogelius

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1988)

  • Volume: 22, Issue: 1, page 53-74
  • ISSN: 0764-583X

How to cite

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Damlamian, Alain, and Vogelius, Michael. "Homogenization limits of diffusion equations in thin domains." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 22.1 (1988): 53-74. <http://eudml.org/doc/193523>.

@article{Damlamian1988,
author = {Damlamian, Alain, Vogelius, Michael},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {composite medium; thin n-dimensional domain; horizontally periodic; mixture; two isotropic components; geometry independent optimal; bounds},
language = {eng},
number = {1},
pages = {53-74},
publisher = {Dunod},
title = {Homogenization limits of diffusion equations in thin domains},
url = {http://eudml.org/doc/193523},
volume = {22},
year = {1988},
}

TY - JOUR
AU - Damlamian, Alain
AU - Vogelius, Michael
TI - Homogenization limits of diffusion equations in thin domains
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1988
PB - Dunod
VL - 22
IS - 1
SP - 53
EP - 74
LA - eng
KW - composite medium; thin n-dimensional domain; horizontally periodic; mixture; two isotropic components; geometry independent optimal; bounds
UR - http://eudml.org/doc/193523
ER -

References

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  1. [1] D CAILLERIE, Homogénéisation des équations de la diffusion stationnaire dans les domaines cylindriques aplatis R A I R O Analyse Numérique, 15 (1981), pp 295-319 Zbl0483.35003MR642495
  2. [2] D CAILLERIE, Thin elastic and periodic plates Math Methods Appl Sci , 6 (1984), pp 159-191 Zbl0543.73073MR751739
  3. [3] A DAMLAMIAN, M VOGELIUS, Homogenization limits of the equations of elasticity in thin domains SIAM J Math Anal , 18 (2) (1987), pp 435-451 Zbl0614.73012MR876283
  4. [4] E DE GIORGI, Quelques problèmes de Γ -convergence, in proceedings of the Conference Computing Methods in Applied Sciences and Engineering, Versailles 1979 (R Glowinski and J L Lions eds ), North Holland, 1980, pp 637-643 Zbl0445.49018MR584059
  5. [5] R KOHN - G W MILTON, On bounding the effective conductivity of anisotropic composites, in Homogenization and Effective Moduli of Materials and Media (J R Ericksen, D Kinderlehrer, R Kohn, J L Lions eds ) IMA Volumes in Math Appls, 1, Springer, 1986, pp 97-125 Zbl0631.73012MR859413
  6. [6] R KOHN, M VOGELIUS, A new model for thin plates with rapidly varying thickness II a convergence proof Quart Appl Math , 43 (1985) pp 1-22 Zbl0565.73046MR782253
  7. [7] K A LURIE, A V CHERKAEV, Exact estimates of the conductivity of composites formed by two isotropically conducting media taken in prescribed proportions Proc Royal Soc Edinburgh, 99A (1984), pp 71-87 Zbl0564.73079MR781086
  8. [8] F MURAT, H-convergence, Séminaire d'Analyse Fonctionnelle et Numérique 1977/1978 Département de Mathématiques, Université d'Alger 
  9. [9] F MURAT, G FRANCFORT, Homogenization and optimal bounds in linear elasticity Arch Rat Mech Anal , 94 (1986), pp 307-334 Zbl0604.73013MR846892
  10. [10] L TARTAR, Cours Peccot, Collège de France, Paris, 1977 
  11. [11] L TARTAR, Estimations fines des coefficients homogénéises, in Ennio De Giorgi's Colloquium (P Kree ed), Pitman Research Notes in Math, Pitman, 1985 Zbl0586.35004MR909716

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