@article{COCV_1999__4__209_0, author = {Allaire, Gr\'egoire and Amar, Micol}, title = {Boundary layer tails in periodic homogenization}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {209--243}, publisher = {EDP-Sciences}, volume = {4}, year = {1999}, mrnumber = {1696289}, zbl = {0922.35014}, language = {en}, url = {http://www.numdam.org/item/COCV_1999__4__209_0/} }
TY - JOUR AU - Allaire, Grégoire AU - Amar, Micol TI - Boundary layer tails in periodic homogenization JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 1999 SP - 209 EP - 243 VL - 4 PB - EDP-Sciences UR - http://www.numdam.org/item/COCV_1999__4__209_0/ LA - en ID - COCV_1999__4__209_0 ER -
Allaire, Grégoire; Amar, Micol. Boundary layer tails in periodic homogenization. ESAIM: Control, Optimisation and Calculus of Variations, Volume 4 (1999), pp. 209-243. http://www.numdam.org/item/COCV_1999__4__209_0/
[1] Diffraction at a curved grating, TM and TE cases, homogenization. J. Math. Anal. Appl. 202 ( 1996) 995-1206. | MR | Zbl
and ,[2] Effect d'un revêtement métallisé mince sur la réflexion d'une onde électromagnétique. C.R. Acad. Sci. Paris Sér. I Math. 314 ( 1992) 217-222. | MR | Zbl
,[3] Domain decomposition and wall laws. C.R. Acad. Sci. Paris Sér. I Math. 320 ( 1995) 541-547. | MR | Zbl
and ,[4] A 2nd order condition for flow over rough walls, in Proc. Int. Conf. on Nonlinear Diff. Eqs. and Appl., Bangalore, Shrikant Ed. ( 1996).
and ,[5] Homogenization of the criticality spectral equation in neutron transport. M2AN to appear. | Numdam | MR | Zbl
and ,[6] Bloch wave homogenization and spectral asymptotic analysis. J. Math. Pures et Appl. 77 ( 1998) 153-208. | MR | Zbl
and ,[7] Boundary layers in the homogenization of a spectral problem in fluid-solid structures. SIAM J. Math. Anal. 29 ( 1998) 343-379. | MR | Zbl
and ,[8] Homogenization of elliptic problems with Lp boundary data. Appl. Math. Optim. 15 ( 1987) 93-107. | MR | Zbl
and ,[9] Compactness methods in the theory of homogenization. C.P.A.M., XL ( 1987) 803-847. | MR | Zbl
and ,[10] Solution of interface problems by homogenization I, II, III. SIAM J. Math. Anal. 7 ( 1976) 603-634 and 635-645; 8 ( 1977) 923-937. | MR | Zbl
,[11] Homogenization, averaging processes in periodic media. Kluwer Academic Publishers, Dordrecht, Mathematics and its Applications 36 ( 1990). | MR | Zbl
and ,[12] First-order corrector for the homogenization of the criticality eigenvalue problem in the even parity formulation of the neutron transport, to appear. | MR | Zbl
,[13] Asymptotic analysis for periodic structures. North Holland, Amsterdam ( 1978). | MR | Zbl
, and ,[14] Boundary layers and homogenization of transport processes. Publ. Res. Inst. Math. Sci. 15 ( 1979) 53-157. | MR | Zbl
, and ,[15] Non-linear effects for flow in periodically constricted channel caused by high injection rate. Mathematical Models and Methods in Applied Sciences 8 ( 1998) 379-405. | MR | Zbl
and ,[16] Homogénéisation de frontière. PhD Thesis, Université de Nice ( 1978.
and ,[17] Reinforcement by a thin layer with oscillating thickness. Appl. Math. Optim. 16 ( 1987) 247-261. | MR
and ,[18] The boundary-value problem in domains with very rapidly oscillating boundary. INRIA Report 3062 ( 1996).
, and ,[19] Analyse mathématique et calcul numérique, Tome 3, Masson, Paris ( 1984). | MR
and ,[20] Effective boundary conditions for accoustic and electro-magnetic scaterring in thin layers. Internal report 278, CMAP Ecole Polytechnique ( 1993).
and ,[21] A boundary value problem for the Poisson equation with multi-scale oscillating boundary. J. Diff. Eq. 137 ( 1997) 54-93. | MR | Zbl
, and ,[22] On the boundary conditions at the contact interface between a porous medium and a free fluid. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 23 ( 1996) 403-465. | Numdam | MR | Zbl
and ,[23] A theorem on the asymptotics of solutions of elliptic equations with coefficients periodic in all variables except one. Soviet Math. Dokl. 18 ( 1977) 1140-1143. | Zbl
and ,[24] Some methods in the mathematical analysis of systems and their controls. Science Press, Beijing, Gordon and Breach, New York ( 1981). | MR | Zbl
,[25] First order corrections to the homogenized eigenvalues of a periodic composite medium. A convergence proof. Proc. Roy. Soc. Edinburg 127 ( 1997) 1263-1295. | MR | Zbl
and ,[26] Mathematical problems in elasticity and homogenization. North Holland, Amsterdam ( 1992). | MR | Zbl
, and ,[27] Non homogeneous media and vibration theory. Springer Verlag, Lecture notes in physics 127 ( 1980). | MR | Zbl
,[28] A dispersive effective medium for wave propagation in periodic composites. SIAM J. Appl. Math. 51 ( 1991) 984-1005. | MR | Zbl
and ,[29] First-order corrections to the homogenized eigenvalues of a periodic composite medium. SIAM J. Appl. Math. 53 ( 1993) 1636-1668. | MR | Zbl
and ,