EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 44 / No 3 (May-June 2010) ESAIM: M2AN, 44 3 (2010) 421-454 References
Free Access
Issue
ESAIM: M2AN
Volume 44, Number 3, May-June 2010
Page(s) 421 - 454
DOI https://doi.org/10.1051/m2an/2010008
Published online 04 February 2010
  1. J.L. Auriault and H. Ene, Macroscopic modelling of heat transfer in composites with interfacial thermal barrier. International J. Heat Mass Transfer 37 (1994) 2885–2892. [CrossRef] [Google Scholar]
  2. A. Bensoussan, J.L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures. North-Holland, Amsterdam (1978). [Google Scholar]
  3. S. Brahim-Otsman, G.A. Francfort and F. Murat, Correctors for the homogenization of the wave and heat equations. J. Math. Pures Appl. 8 (1992) 197–231. [Google Scholar]
  4. M. Briane, A. Damlamian and P. Donato, H-convergence in Perforated Domains, in Nonlinear Partial Differential Equations and Their Applications – Collège de France Seminar XIII, D. Cioranescu and J.L. Lions Eds., Pitman Research Notes in Mathematics Series 391, Longman, New York, USA (1998) 62–100. [Google Scholar]
  5. H.S. Carslaw and J.C. Jaeger, Conduction of heat in solids. The Clarendon Press, Oxford, UK (1947). [Google Scholar]
  6. D. Cioranescu and P. Donato, Homogénéisation du problème de Neumann non homogène dans des ouverts perforés. Asymptot. Anal. 1 (1988) 115–138. [Google Scholar]
  7. D. Cioranescu and P. Donato, Exact internal controllability in perforated domains. J. Math. Pures Appl. 68 (1989) 185–213. [MathSciNet] [Google Scholar]
  8. D. Cioranescu and P. Donato, An Introduction to Homogenization, Oxford Lecture Series in Mathematics and its Applications 17. Oxford Univ. Press, New York, USA (1999). [Google Scholar]
  9. D. Cioranescu and J. Saint Jean Paulin, Homogenization in open sets with holes. J. Math. Anal. Appl. 71 (1979) 590–607. [CrossRef] [MathSciNet] [Google Scholar]
  10. D. Cioranescu and J. Saint Jean Paulin, Homogenization of Reticulated Structures. Springer-Verlag, New York (1999). [Google Scholar]
  11. D. Cioranescu, P. Donato, F. Murat and E. Zuazua, Homogenization and corrector for the wave equation in domains with small holes. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 2 (1999) 251–293. [Google Scholar]
  12. P. Donato, Some corrector results for composites with imperfect interface. Rend. Math. Ser. VII 26 (2006) 189–209. [Google Scholar]
  13. P. Donato and S. Monsurrò, Homogenization of two heat conductors with an interfacial contact resistance. Anal. Appl. 2 (2004) 1–27. [CrossRef] [Google Scholar]
  14. P. Donato and A. Nabil, Approximate controllability of linear parabolic equations in perforated domains. ESAIM: COCV 6 (2001) 21–38. [CrossRef] [EDP Sciences] [Google Scholar]
  15. P. Donato and A. Nabil, Homogenization and correctors for the heat equation in perforated domains. Chin. Ann. Math. B 25 (2004) 143–156. [CrossRef] [Google Scholar]
  16. P. Donato, A. Gaudiello and L. Sgambati, Homogenization of bounded solutions of elliptic equations with quadratic growth in periodically perforated domains. Asymptot. Anal. 16 (1998) 223–243. [MathSciNet] [Google Scholar]
  17. P. Donato, L. Faella and S. Monsurrò, Homogenization of the wave equation in composites with imperfect interface: a memory effect. J. Math. Pures Appl. 87 (2007) 119–143. [CrossRef] [MathSciNet] [Google Scholar]
  18. P. Donato, L. Faella and S. Monsurrò, Correctors for the homogenization of a class of hyperbolic equations with imperfect interfaces. SIAM J. Math. Anal. 40 (2009) 1952–1978. [CrossRef] [Google Scholar]
  19. L. Faella and S. Monsurrò, Memory Effects Arising in the Homogenization of Composites with Inclusions, Topics on Mathematics for Smart Systems. World Sci. Publ., Hackensack, USA (2007) 107–121. [Google Scholar]
  20. H.K. Hummel, Homogenization for heat transfer in polycrystals with interfacial resistances. Appl. Anal. 75 (2000) 403–424. [CrossRef] [MathSciNet] [Google Scholar]
  21. E. Jose, Homogenization of a parabolic problem with an imperfect interface. Rev. Roumaine Math. Pures Appl. 54 (2009) 189–222. [MathSciNet] [Google Scholar]
  22. J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Volume 1. Dunod, Paris, France (1968). [Google Scholar]
  23. R. Lipton, Heat conduction in fine scale mixtures with interfacial contact resistance . SIAM J. Appl. Math. 58 (1998) 55–72. [CrossRef] [MathSciNet] [Google Scholar]
  24. R. Lipton and B. Vernescu, Composite with imperfect interface. Proc. Soc. Lond. A 452 (1996) 329–358. [CrossRef] [Google Scholar]
  25. M.L. Mascarenhas, Linear homogenization problem with time dependent coefficient. Trans. Amer. Math. Soc. 281 (1984) 179–195. [CrossRef] [MathSciNet] [Google Scholar]
  26. S. Monsurrò, Homogenization of a two-component composite with interfacial thermal barrier. Adv. Math. Sci. Appl. 13 (2003) 43–63. [MathSciNet] [Google Scholar]
  27. S. Monsurrò, Erratum for the paper “Homogenization of a two-component composite with interfacial thermal barrier” (in Vol. 13, pp. 43–63, 2003). Adv. Math. Sci. Appl. 14 (2004) 375–377. [MathSciNet] [Google Scholar]
  28. S.E. Pastukhova, Homogenization of nonstationary problems in the theory of elasticity on thin periodic structures from the standpoint of the convergence of hyperbolic semigroups in a variable Hilbert space. Sovrem. Mat. Prilozh. 16, Differ. Uravn. Chast. Proizvod. (2004) 64–97 (Russian). Translation in J. Math. Sci. (N. Y.) 133 (2006) 949–998. [Google Scholar]
  29. R.E. Showalter, Distributed microstructure models of porous media, in Flow in porous media (Oberwolfach (1992)), J. Douglas and U. Hornung Eds., Internat. Ser. Numer. Math. 114, Birkhäuser, Basel, Switzerland (1993) 155–163. [Google Scholar]
  30. L. Tartar, Cours Peccot. Collège de France, France, unpublished (1977). [Google Scholar]
  31. L. Tartar, Quelques remarques sur l'homogénéisation, in Functional Analysis and Numerical Analysis, Proc. Japan-France Seminar 1976, Japanese Society for the Promotion of Science (1978) 468–482. [Google Scholar]
  32. L. Tartar, Memory effects and homogenization. Arch. Rational Mech. Anal. 3 (1990) 121–133. [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.

Recommended for you