@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://archive.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://archive.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://archive.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://archive.numdam.org/item/M2AN_1991__25_6_693_0/
[1] Sulla convergenza degli integrali dell'energia per operatori ellitici del secundo ordine, Boll. I.M.I., 8, 391-411, 1973. | MR | Zbl
and ,[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] Asymptotic Analysis for Periodic Structures, North Holland, Amsterdam, 1978. | MR | Zbl
, and ,[5] Nonhomogeneous Media and Vibration Theory, Springer, 1980. | MR | Zbl
,[6] 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
and ,[7] AVERAGING and G-convergence of differential operators, Uspekhi Mat. Nauk. 34, 65-133, 1979. | MR | Zbl
, , and ,[8] Average of processes in periodic media, Nauka, Moscow, 1984. | Zbl
and ,[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] 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
and ,[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] Particle method approximation of oscillatory solutions to hyperbolic differential equations, SIAM J. Numer. Anal. 26, 289-319, 1989. | MR | Zbl
and ,[15] Computation of oscillatory solutions to hyperbolic differential equations using particle methods, Lecture Notes in Math., 1360, 68-82, 1988. | MR | Zbl
and ,[16] Solutions oscillantes des équations de Carleman, Séminaire Goulaouic-Meyer-Schwartz, 1981. | Numdam | MR | Zbl
,[17] Weak limits of semilinear hyperbolic equations with oscillating data, Springer Lecture Notes in Phys., 230, 277-289, 1985. | Zbl
, and ,[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] Diffusive behavior of a random walk in a random medium, in « Stochastic Analysis » by K. Ito, 105-120, North Holland, 1984. | MR | Zbl
, and ,[20] Ergodic Problems of Classical Mechanics, Benjamin, New York, 1968. | MR | Zbl
and ,[21] Bounds for effective parameters of heterogeneous media by analytic continuation, Comm. Math. Phys., 90, 473-491, 1983. | MR
and ,