no. 4
Homogenization of the criticality spectral equation in neutron transport
ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 4, pp. 721-746 
@article{M2AN_1999__33_4_721_0,
     author = {Allaire, Gr\'egoire and Bal, Guillaume},
     title = {Homogenization of the criticality spectral equation in neutron transport},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {721--746},
     year = {1999},
     publisher = {EDP Sciences},
     volume = {33},
     number = {4},
     mrnumber = {1726482},
     zbl = {0931.35010},
     language = {en},
     url = {https://www.numdam.org/item/M2AN_1999__33_4_721_0/}
}
TY  - JOUR
AU  - Allaire, Grégoire
AU  - Bal, Guillaume
TI  - Homogenization of the criticality spectral equation in neutron transport
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1999
SP  - 721
EP  - 746
VL  - 33
IS  - 4
PB  - EDP Sciences
UR  - https://www.numdam.org/item/M2AN_1999__33_4_721_0/
LA  - en
ID  - M2AN_1999__33_4_721_0
ER  - 
%0 Journal Article
%A Allaire, Grégoire
%A Bal, Guillaume
%T Homogenization of the criticality spectral equation in neutron transport
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1999
%P 721-746
%V 33
%N 4
%I EDP Sciences
%U https://www.numdam.org/item/M2AN_1999__33_4_721_0/
%G en
%F M2AN_1999__33_4_721_0
Allaire, Grégoire; Bal, Guillaume. Homogenization of the criticality spectral equation in neutron transport. ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 4, pp. 721-746. https://www.numdam.org/item/M2AN_1999__33_4_721_0/

[1] R. Alexandre and K. Hamdache, Homogénéisation d'équations cinétiques en milieu perforé. C.R. Acad. Sci. Paris Sér. I 313 (1991) 339-344. | Zbl | MR

[2] G. Allaire, Homogenization and two scale convergence. SIAM J. Math. Anal. 23 (1992) 1482-1518. | Zbl | MR

[3] G. Allaire and G. Bal, Homogénéisation d'une équation spectrale de transport neutronique. C.R. Acad. Sci. Paris Sér. I 325 (1997) 1043-1048. | Zbl | MR

[4] G. Allaire and Y. Capdeboscq, Homogenization of a spectral problem for a multigroup neutronic diffusion model. Comput Methods Appl. Mech. Engrg. (to appear). | Zbl | MR

[5] G. Allaire and F. Malige, Analyse asymptotique spectrale d'un problème de diffusion neutronique. C.R. Acad. Sci. Paris Sér. I 324 (1997) 939-944. | Zbl | MR

[6] P. Anselone, Collectively compact operator approximation theory and applications to integral equations. Prentice-Hall Englewood Cliffs, N.J. (1971). | Zbl | MR

[7] G. Bal, Couplage d'équations et homogénéisation en transport neutronique. Ph.D. thesis, University of Paris 6, France (1997).

[8] G. Bal, First-order Corrector for the Homogenization of the Criticality Eigenvalue Problem in the Even Parity Formulation of the Neutron Transport. SIAM J. Appl. Math, (to appear). | Zbl | MR

[9] G. Bal and X. Warin, An asymptotic analysis for the homogenization of P.W.R. assemblies - The transport case -. Nuclear Sci. Engng. (submitted).

[10] P. Benoist, Théorie du coefficient de diffusion des neutrons dans un réseau comportant des cavités. Note CEA-R 2278 (1964).

[11] A. Bensoussan, J.L. Lions and G. Papanicolaou, Boundary layers and homogenization of transport processes. Publ. RIMS Kyoto Univ. (1979) 53-157. | Zbl | MR

[12]J. Bussac and P. Reuss, Traité de neutronique. Hermann, Paris (1978).

[13] F. Chatelin, Spectral approximation of linear operators. Academic Press (1983). | Zbl | MR

[14] R. Dautray and J.L. Lions, Mathematical analysis and numerical methods for Science and Technology, Vol. 6. Springer Verlag, Berlin (1993). | Zbl | MR

[15] V. Deniz, The theory of neutron leakage in reactor lattices, in Handbook of nuclear reactor calculations. Vol II, Y. Ronen Ed. (1968) 409-508.

[16] L. Dumas and F. Golse, Homogenization of transport equations. Preprint No. R98003, University of Paris 6, LAN. | Zbl | MR

[17] E. Frenod and K. Hamdache, Homogenization of transport kinetic equation with oscillating potentials. Proc. Roy. Soc. Edin-burgh Sect. A 126 (1996) 1247-1275. | Zbl | MR

[18] 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. | Zbl | MR

[19] T. Goudon and F. Poupaud (personal communication).

[20] E. Larsen, Neutron transport and diffusion in inhomogeneous media I. J. Math. Phys. 16 (1975) 1421-1427. | MR

[21] E. Larsen, Neutron transport and diffusion in inhomogeneous media II. Nuclear Sci. Engng. 60 (1976) 357-368.

[22] E. Larsen and J. Keiler, Asymptotic solution of neutron transport problems for small mean free paths. J. Math. Phys. 15 (1974) 75-81. | MR

[23] E. Larsen and M. Williams, Neutron Drift in Heterogeneous Media. Nuclear Sci. Engng. 65 (1978) 290-302.

[24] F. Malige, Étude mathématique et numérique de l'homogénéisation des assemblages combustibles d'un coeur de réacteur nucléaire. Ph.D. thesis, École Polytechnique, France (1996).

[25] M. Mokhtar-Kharroubi, Les équations de la neutronique. Ph.D. thesis, University of Paris XIII, France (1987).

[26] G. Nguetseng, A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal. 20 (1989) 608-623. | Zbl | MR

[27] J. Planchard, Méthodes mathématiques en neutronique. Collection de la Direction des Etudes et Recherches d'EDF, Eyrolles (1995).

[28] 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. | Zbl | MR

[29] R. Sentis, Study of the corrector of the eigenvalue of a transport operator. SIAM J. Math. Anal. 16 (1985) 151-166. | Zbl | MR