Free Access
Volume 9, February 2003
Page(s) 371 - 398
Published online 15 September 2003
  1. G. Allaire, Homogenization and two scale convergence. SIAM J. Math. Anal. 23 (1992) 1482-1518. [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]

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.