Free Access
Issue
ESAIM: COCV
Volume 9, March 2003
Page(s) 371 - 398
DOI https://doi.org/10.1051/cocv:2003018
Published online 15 September 2003
  1. G. Allaire, Homogenization and two scale convergence. SIAM J. Math. Anal. 23 (1992) 1482-1518. [CrossRef] [MathSciNet] [Google Scholar]
  2. G. Allaire and G. Bal, Homogenization of the criticality spectral equation in neutron transport. ESAIM: M2AN 33 (1999) 721-746. Announced in Homogénéisation d'une équation spectrale du transport neutronique. CRAS, Vol. 325 (1997) 1043-1048. [CrossRef] [EDP Sciences] [Google Scholar]
  3. G. Allaire, G. Bal and V. Siess, Homogenization and localization in locally periodic transport. ESAIM: COCV 8 (2002) 1-30. [CrossRef] [EDP Sciences] [Google Scholar]
  4. G. Allaire and Y. Capdeboscq, Homogeneization of a spectral problem for a multigroup neutronic diffusion model. Comput. Methods Appl. Mech. Engrg. 187 (2000) 91-117. [CrossRef] [MathSciNet] [Google Scholar]
  5. G. Bal, Couplage d'équations et homogénéisation en transport neutronique. Thèse de doctorat de l'Université Paris 6 (1997). [Google Scholar]
  6. G. Bal, Homogenization of a spectral equation with drift in linear transport. ESAIM: COCV 6 (2001) 613-627. [CrossRef] [EDP Sciences] [Google Scholar]
  7. C. Bardos, F. Golse and B. Perthame, The Rosseland approximation for the radiative transfer equations. CPAM 40 (1987) 691-721; and CPAM 42 (1989) 891-894. [Google Scholar]
  8. C. Bardos, F. Golse, B. Perthame and R. Sentis, The nonaccretive radiative transfer equations: Existence of solutions ans Rosseland approximations. J. Funct. Anal. 77 (1988) 434-460. [CrossRef] [MathSciNet] [Google Scholar]
  9. 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]
  10. H. Brézis, Analyse fonctionnelle, Théorie et applications. Masson (1993). [Google Scholar]
  11. Y. Capdeboscq, Homogenization of a spectral problem with drift. Proc. Roy. Soc. Edinburgh Sect. A 132 (2002) 567-594; Announced in Homogenization of a diffusion equation with drift. CRAS, Vol. 327 (2000) 807-812. [Google Scholar]
  12. Y. Capdeboscq, Homogénéisation des modèles de diffusion en neutronique. Thèse Université Paris 6 (1999). [Google Scholar]
  13. C. Cercignani, The Boltzmann equation and its applications. Springer-Verlag, Appl. Math. Sci. 67 (1988). [Google Scholar]
  14. F. Chalub, P. Markowich, B. Perthame and C. Schmeiser, Kinetic models for chemotaxis and their drift-diffusion limits. Preprint. [Google Scholar]
  15. J.-F. Collet, Work in preparation. Personal communication. [Google Scholar]
  16. R. Dautray and J.-L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques, Vol. 3. Masson (1985). [Google Scholar]
  17. P. Degond, T. Goudon and F. Poupaud, Diffusion limit for non homogeneous and non reversible processes. Indiana Univ. Math. J. 49 (2000) 1175-1198. [MathSciNet] [Google Scholar]
  18. R. Di Perna, P.-L. Lions and Y. Meyer, Formula regularity of velocity averages. Ann. Inst. H. Poincaré Anal. Non Linéaire 8 (1991) 271-287. [Google Scholar]
  19. L. Dumas and F. Golse, Homogenization of transport equations. SIAM J. Appl. Math. 60 (2000) 1447-1470. [CrossRef] [MathSciNet] [Google Scholar]
  20. R. Edwards, Functional analysis, Theory and applications. Dover (1994). [Google Scholar]
  21. L.C. Evans, The perturbed test function method for viscosity solutions of nonlinear PDE. Proc. Roy. Soc. Edinburgh Sect. A 111 (1989) 359-375. [Google Scholar]
  22. L.C. Evans, Periodic homogenisation of certain fully nonlinear partial differential equations. Proc. Roy. Soc. Edinburgh Sect. A 120 (1992) 245-265. [MathSciNet] [Google Scholar]
  23. P. Gérard and F. Golse, Averaging regularity results for pdes under transversality assumptions. Comm. Pure Appl. Math. 45 (1992) 1-26. [CrossRef] [MathSciNet] [Google Scholar]
  24. F. Golse, From kinetic to macroscopic models, in Kinetic equations and asymptotic theory, edited by B. Perthame andL. Desvillettes. Gauthier-Villars, Appl. Math. 4 (2000) 41-121. [Google Scholar]
  25. F. Golse, P.-L. Lions, B. Perthame and R. Sentis, Regularity of the moments of the solution of a transport equation. J. Funct. Anal. 76 (1988) 110-125. [CrossRef] [MathSciNet] [Google Scholar]
  26. F. Golse and F. Poupaud, Limite fluide des équations de Boltzmann des semi-conducteurs pour une statistique de Fermi-Dirac. Asymptot. Anal. 6 (1992) 135-160. [Google Scholar]
  27. T. Goudon and A. Mellet, Diffusion approximation in heterogeneous media. Asymptot. Anal. 28 (2001) 331-358. [MathSciNet] [Google Scholar]
  28. T. Goudon and A. Mellet, On fluid limit for the semiconductors Boltzmann equation. J. Differential Equations (to appear). [Google Scholar]
  29. T. Goudon and F. Poupaud, Approximation by homogeneization and diffusion of kinetic equations. Comm. Partial Differential Equations 26 (2001) 537-569. [CrossRef] [MathSciNet] [Google Scholar]
  30. T. Goudon and F. Poupaud, Homogenization of transport equations; weak mean field approximation. Preprint. [Google Scholar]
  31. M. Krein and M. Rutman, Linear operator leaving invariant a cone in a Banach space. AMS Transl. 10 (1962) 199-325. [Google Scholar]
  32. R. Kubo, H-Theorems for Markoffian Processes, in Perspectives in Statistical Physics, edited by H. Raveché. North Holland (1981). [Google Scholar]
  33. E. Larsen, Neutron transport and diffusion in heterogeneous media (1). J. Math. Phys. (1975) 1421-1427. [Google Scholar]
  34. E. Larsen, Neutron transport and diffusion in heterogeneous media (2). Nuclear Sci. Engrg. (1976) 357-368. [Google Scholar]
  35. E. Larsen and J. Keller, Asymptotic solution of neutron transport processes for small free paths. J. Math. Phys. 15 (1974) 75-81. [CrossRef] [Google Scholar]
  36. E. Larsen and M. Williams, Neutron drift in heterogeneous media. Nuclear Sci. Engrg. 65 (1978) 290-302. [Google Scholar]
  37. P.-L. Lions and G. Toscani, Diffuse limit for finite velocity Boltzmann kinetic models. Rev. Mat. Ib. 13 (1997) 473-513. [Google Scholar]
  38. G. Nguetseng, A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal. 20 (1989) 608-623. [CrossRef] [MathSciNet] [Google Scholar]
  39. R. Petterson, Existence theorems for the linear, space-inhomogeneous transport equation. IMA J. Appl. Math. 30 (1983) 81-105. [CrossRef] [MathSciNet] [Google Scholar]
  40. F. Poupaud, Diffusion approximation of the linear semiconductor Boltzmann equation: Analysis of boundary layers. Asymptot. Anal. 4 (1991) 293-317. [Google Scholar]
  41. E. Ringeisen and R. Sentis, On the diffusion approximation of a transport process without time scaling. Asymptot. Anal. 5 (1991) 145-159. [Google Scholar]
  42. L. Tartar, Remarks on homogenization, in Homogenization and effective moduli of material and media. Springer, IMA Vol. in Math. and Appl. (1986) 228-246. [Google Scholar]
  43. E. Wigner, Nuclear reactor theory. AMS (1961). [Google Scholar]

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