@article{M2AN_1991__25_6_693_0,
author = {Avellaneda, M. and Hou, Th. Y. and Papanicolaou, G. C.},
title = {Finite difference approximations for partial differential equations with rapidly oscillating coefficients},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {693--710},
publisher = {AFCET - Gauthier-Villars},
address = {Paris},
volume = {25},
number = {6},
year = {1991},
mrnumber = {1135990},
zbl = {0755.65088},
language = {en},
url = {http://www.numdam.org/item/M2AN_1991__25_6_693_0/}
}
TY - JOUR AU - Avellaneda, M. AU - Hou, Th. Y. AU - Papanicolaou, G. C. TI - Finite difference approximations for partial differential equations with rapidly oscillating coefficients JO - ESAIM: Modélisation mathématique et analyse numérique PY - 1991 SP - 693 EP - 710 VL - 25 IS - 6 PB - AFCET - Gauthier-Villars PP - Paris UR - http://www.numdam.org/item/M2AN_1991__25_6_693_0/ LA - en ID - M2AN_1991__25_6_693_0 ER -
%0 Journal Article %A Avellaneda, M. %A Hou, Th. Y. %A Papanicolaou, G. C. %T Finite difference approximations for partial differential equations with rapidly oscillating coefficients %J ESAIM: Modélisation mathématique et analyse numérique %D 1991 %P 693-710 %V 25 %N 6 %I AFCET - Gauthier-Villars %C Paris %U http://www.numdam.org/item/M2AN_1991__25_6_693_0/ %G en %F M2AN_1991__25_6_693_0
Avellaneda, M.; Hou, Th. Y.; Papanicolaou, G. C. Finite difference approximations for partial differential equations with rapidly oscillating coefficients. ESAIM: Modélisation mathématique et analyse numérique, Tome 25 (1991) no. 6, pp. 693-710. http://www.numdam.org/item/M2AN_1991__25_6_693_0/
[1] and , Sulla convergenza degli integrali dell'energia per operatori ellitici del secundo ordine, Boll. I.M.I., 8, 391-411, 1973. | MR | Zbl
[2] , Solution of interface problems by homogenization I, II, III, SIAM J. Math. Analysis, 7, 603-345, 635-645, and 8, 923-937, 1976. | MR | Zbl
[3] , Cours Peccot, Paris 1977.
[4] , and , Asymptotic Analysis for Periodic Structures, North Holland, Amsterdam, 1978. | MR | Zbl
[5] , Nonhomogeneous Media and Vibration Theory, Springer, 1980. | MR | Zbl
[6] and , Boundary value problems with rapidly oscillating random coefficients, at Proceedings of Conference on Random Fields, Esztergom, Hungary, 1979, published in Séria Colloquia Mathematica Societatis Janos Bolyai, 27, 835-873, North Holland, 1981. | MR | Zbl
[7] , , and , AVERAGING and G-convergence of differential operators, Uspekhi Mat. Nauk. 34, 65-133, 1979. | MR | Zbl
[8] and , Average of processes in periodic media, Nauka, Moscow, 1984. | Zbl
[9] , The method of averaging and walks in inhomogeneous environments, Uspekhi Mat. Nauk 40, 61-120, 1985. | MR | Zbl
[10] , Macroscopic properties of composites, bubbly fluids, suspensions and related problems, in Les méthodes de Fhomogénéization : Théorie et applications en physique, CEA-EDF-INRIA séries 57, 229-318, Eyrolles, Paris, 1985. | MR
[11] , Remarques sur les problèmes d'homogénéization dans les milieux à structure périodique et sur quelques problèmes raides, in Les méthodes de l'homogénéization : Théorie et applications en physique, CEA-EDF-INRIA séries 57, 129-228, Eyrolles, Paris, 1985. | MR
[12] and , Calcul des variations et homogénéization, in Les méthodes de l'homogénéization : Théorie et applications en physique, CEA-EDF-INRIA séries 57, 319-370, Eyrolles, Paris, 1985. | MR
[13] , Computation of oscillatory solutions to hyperbolic differential equations, to appear. Also in Lecture Notes in Math. 1270, 10-22, Springer, 1987. | MR | Zbl
[14] and , Particle method approximation of oscillatory solutions to hyperbolic differential equations, SIAM J. Numer. Anal. 26, 289-319, 1989. | MR | Zbl
[15] and , Computation of oscillatory solutions to hyperbolic differential equations using particle methods, Lecture Notes in Math., 1360, 68-82, 1988. | MR | Zbl
[16] , Solutions oscillantes des équations de Carleman, Séminaire Goulaouic-Meyer-Schwartz, 1981. | Numdam | MR | Zbl
[17] , and, Weak limits of semilinear hyperbolic equations with oscillating data, Springer Lecture Notes in Phys., 230, 277-289, 1985. | Zbl
[18] , The diffusion limit for reversible jump processes on Zd with ergodic random bond conductivities, Comm. Math. Phys., 90, 27-68, 1983. | MR | Zbl
[19] , and , Diffusive behavior of a random walk in a random medium, in « Stochastic Analysis » by K. Ito, 105-120, North Holland, 1984. | MR | Zbl
[20] and , Ergodic Problems of Classical Mechanics, Benjamin, New York, 1968. | MR | Zbl
[21] and , Bounds for effective parameters of heterogeneous media by analytic continuation, Comm. Math. Phys., 90, 473-491, 1983. | MR
