Free Access
Volume 4, 1999
Page(s) 209 - 243
Published online 15 August 2002
  1. T. Abboud and H. Ammari, Diffraction at a curved grating, TM and TE cases, homogenization. J. Math. Anal. Appl. 202 (1996) 995-1206. [CrossRef] [MathSciNet] [Google Scholar]
  2. Y. Achdou, 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. [Google Scholar]
  3. Y. Achdou and O. Pironneau, Domain decomposition and wall laws. C.R. Acad. Sci. Paris Sér. I Math. 320 (1995) 541-547. [Google Scholar]
  4. Y. Achdou and O. Pironneau, A 2nd order condition for flow over rough walls, in Proc. Int. Conf. on Nonlinear Diff. Eqs. and Appl., Bangalore, Shrikant Ed. (1996). [Google Scholar]
  5. G. Allaire and G. Bal, Homogenization of the criticality spectral equation in neutron transport. M2AN to appear. [Google Scholar]
  6. G. Allaire and C. Conca, Bloch wave homogenization and spectral asymptotic analysis. J. Math. Pures et Appl. 77 (1998) 153-208. [Google Scholar]
  7. G. Allaire and C. Conca, Boundary layers in the homogenization of a spectral problem in fluid-solid structures. SIAM J. Math. Anal. 29 (1998) 343-379. [Google Scholar]
  8. M. Avellaneda and F.-H. Lin, Homogenization of elliptic problems with Lp boundary data. Appl. Math. Optim. 15 (1987) 93-107. [CrossRef] [MathSciNet] [Google Scholar]
  9. M. Avellaneda and F.-H. Lin, Compactness methods in the theory of homogenization. C.P.A.M., XL (1987) 803-847. [Google Scholar]
  10. I. Babuška, Solution of interface problems by homogenization I, II, III. SIAM J. Math. Anal. 7 (1976) 603-634 and 635-645; 8 (1977) 923-937. [Google Scholar]
  11. N. Bakhvalov and G. Panasenko, Homogenization, averaging processes in periodic media. Kluwer Academic Publishers, Dordrecht, Mathematics and its Applications 36 (1990). [Google Scholar]
  12. G. Bal, First-order corrector for the homogenization of the criticality eigenvalue problem in the even parity formulation of the neutron transport, to appear. [Google Scholar]
  13. A. Bensoussan, J.L. Lions and G. Papanicolaou, Asymptotic analysis for periodic structures. North Holland, Amsterdam (1978). [Google Scholar]
  14. A. Bensoussan, J.L. Lions and G. Papanicolaou, Boundary layers and homogenization of transport processes. Publ. Res. Inst. Math. Sci. 15 (1979) 53-157. [CrossRef] [MathSciNet] [Google Scholar]
  15. A. Bourgeat and E. Marusic-Paloka, 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. [CrossRef] [MathSciNet] [Google Scholar]
  16. R. Brizzi and J.P. Chalot, Homogénéisation de frontière. PhD Thesis, Université de Nice (1978). [Google Scholar]
  17. G. Buttazzo and R.V. Kohn, Reinforcement by a thin layer with oscillating thickness. Appl. Math. Optim. 16 (1987) 247-261. [CrossRef] [MathSciNet] [Google Scholar]
  18. G. Chechkin, A. Friedman and A. Piatnitski, The boundary-value problem in domains with very rapidly oscillating boundary. INRIA Report 3062 (1996). [Google Scholar]
  19. R. Dautray and J.-L. Lions, Analyse mathématique et calcul numérique, Tome 3, Masson, Paris (1984). [Google Scholar]
  20. B. Engquist and J.C. Nédélec, Effective boundary conditions for accoustic and electro-magnetic scaterring in thin layers. Internal report 278, CMAP École Polytechnique (1993). [Google Scholar]
  21. A. Friedman, B. Hu and Y. Liu, A boundary value problem for the Poisson equation with multi-scale oscillating boundary. J. Diff. Eq. 137 (1997) 54-93. [CrossRef] [Google Scholar]
  22. W. Jäger and A. Mikelic, 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. [MathSciNet] [Google Scholar]
  23. E. Landis and G. Panasenko, 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. [Google Scholar]
  24. J.L. Lions, Some methods in the mathematical analysis of systems and their controls. Science Press, Beijing, Gordon and Breach, New York (1981). [Google Scholar]
  25. S. Moskow and M. Vogelius, First order corrections to the homogenized eigenvalues of a periodic composite medium. A convergence proof. Proc. Roy. Soc. Edinburg 127 (1997) 1263-1295. [Google Scholar]
  26. O. Oleinik, A. Shamaev and G. Yosifian, Mathematical problems in elasticity and homogenization. North Holland, Amsterdam (1992). [Google Scholar]
  27. E. Sánchez-Palencia, Non homogeneous media and vibration theory. Springer Verlag, Lecture notes in physics 127 (1980). [Google Scholar]
  28. F. Santosa and W. Symes, A dispersive effective medium for wave propagation in periodic composites. SIAM J. Appl. Math. 51 (1991) 984-1005. [CrossRef] [MathSciNet] [Google Scholar]
  29. F. Santosa and M. Vogelius, First-order corrections to the homogenized eigenvalues of a periodic composite medium. SIAM J. Appl. Math. 53 (1993) 1636-1668. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.