Homogenization and corrector for the wave equation in domains with small holes
D. Cioranescu; P. Donato; F. Murat; E. Zuazua
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1991)
- Volume: 18, Issue: 2, page 251-293
- ISSN: 0391-173X
Access Full Article
topHow to cite
topCioranescu, D., et al. "Homogenization and corrector for the wave equation in domains with small holes." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 18.2 (1991): 251-293. <http://eudml.org/doc/84101>.
@article{Cioranescu1991,
author = {Cioranescu, D., Donato, P., Murat, F., Zuazua, E.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {perforated domains with small holes},
language = {eng},
number = {2},
pages = {251-293},
publisher = {Scuola normale superiore},
title = {Homogenization and corrector for the wave equation in domains with small holes},
url = {http://eudml.org/doc/84101},
volume = {18},
year = {1991},
}
TY - JOUR
AU - Cioranescu, D.
AU - Donato, P.
AU - Murat, F.
AU - Zuazua, E.
TI - Homogenization and corrector for the wave equation in domains with small holes
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1991
PB - Scuola normale superiore
VL - 18
IS - 2
SP - 251
EP - 293
LA - eng
KW - perforated domains with small holes
UR - http://eudml.org/doc/84101
ER -
References
top- [1] S. Brahim-Otsmane - G.A. Francfort - F. Murat, Correctors for the homogenization of the wave and heat equations, J. Math. Pures Appl., to appear. Zbl0837.35016MR1172450
- [2] H. Brezis - F.E. Browder, Some properties of higher order Sobolev spaces, J. Math. Pures Appl., 61 (1982), 242-259. Zbl0512.46034MR690395
- [3] D. Cioranescu - P. Donato, Exact internal controllability in perforated domains, J. Math. Pures Appl., 68 (1989), 185-213. Zbl0627.35057MR1010768
- [4] D. Cioranescu - P. Donato - E. Zuazua, Contrôlabilité exacte frontière de l'équation des ondes dans des domaines perforés avec des petits trous, C.R. Acad. Sci. Paris, 309I (1989), 473-478. Zbl0694.49003MR1055461
- [5] D. Cioranescu - P. Donato - E. Zuazua, Exact boundary controllability for the wave equation in domains with small holes, J. Math. Pures Appl., to appear. Zbl0843.35009MR1055461
- [6] D. Cioranescu - F. Murat, Un terme étrange venu d'ailleurs, in Nonlinear Partial Differential Equations and their Applications, Collège de France Seminar, Vol. II and III, ed. by H. Brezis and J.-L. Lions, Research Notes in Mathematics, 60 and 70, Pitman, London, 1982, 93-138 and 154-178. Zbl0496.35030MR670272
- [7] J. Deny, Les potentiels d'énergie finie, Acta Math., 82 (1950), 107-183. Zbl0034.36201MR36371
- [8] J. Diestel - J.J. Uhl, Vector Measures, Math. Surveys Monographs, 15, Amer. Math. Soc., Providence, RI, 1977. Zbl0369.46039MR453964
- [9] J. Frehse, Capacity Methods in the Theory of Partial Differential Equations, Iber. d. Dt. Math.-Verein, 84 (1982), 1-44. Zbl0486.35002MR644068
- [10] M. Grun-Rehomme, Caractérisation du sous-différentiel d'intégrandes convexes dans les espaces de Sobolev, J. Math. Pures Appl., 56 (1977), 149-156. Zbl0314.35001MR493658
- [11] H. Kacimi, Homogénéisation de problèmes de Dirichlet avec des petits trous, Thèse de 3ème cycle, Université Paris VI, 1987.
- [12] H. Kacimi - F. Murat, Estimation de l'erreur dans des problèmes de Dirichlet où apparaît un terme étrange, in Partial Differential Equations and the Calculus of Variations, Vol. II, Essays in Honor of Ennio de Giorgi, ed. by F. Colombini, A. Marino, L. Modica and S. Spagnolo, Birkhäuser, Boston, 1989, 661-693. Zbl0687.35007MR1034018
- [13] H. Lewy - G. Stampacchia, On the regularity of the solution of a variational inequality, Comm. Pure Appl. Math., 22 (1969), 153-188. Zbl0167.11501MR247551
- [14] J.-L. Lions, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués. Tome 1: Contrôlabilité exacte, R.M.A. 8, Masson, Paris, 1988. Zbl0653.93002MR953547
- [15] J.-L. Lions, Contrôlabilité exacte et homogénéisation (I), Asymptotic Anal., 1 (1988), 3-11. Zbl0659.49002MR932803
- [16] J.-L. Lions - E. Magenes, Problèmes aux limites non homogènes et applications, Vol. 1, Dunod, Paris, 1968. Zbl0165.10801MR247243
- [17] J. Simon, Compact sets in the space Lp(0,T;B), Ann. Mat. Pura Appl., 146IV (1987), 65-96. Zbl0629.46031MR916688
- [18] L. Tartar, Cours Peccot, Collège de France, (1977), partially written in: F. Murat, H-Convergence, Séminaire d'analyse fonctionnelle et numérique de l'Université d'Alger, 1978, duplicated, 34 p.
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.