Homogenization of a spectral equation with drift in linear transport

ESAIM - Control, Optimisation and Calculus of Variations

Volumn 6, Issue , 2001, Pages 613-627

  Bal, Guillaume ^a  

^a UNIVERSITY OF CHICAGO   (United States)

Author keywords

Drift; Eigenvalue problem; Homogenization; Linear transport

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; EIGENVALUES AND EIGENFUNCTIONS; PHASE SPACE METHODS; PROBLEM SOLVING; VELOCITY;

DRIFT; HOMOGENIZATION; LINEAR TRANSPORT; SPECTRAL EQUATION;

LINEAR EQUATIONS;

EID: 0035690766     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv:2001125     Document Type: Article

References (30)

1. G. Allaire, Homogenization and two-scale convergence. SIAM J. Math. Anal. 9 (1992) 1482-1518.
2. G. Allaire and G. Bal, Homogenization of the criticality spectral equation in neutron transport. ESAIM: M2AN 33 (1999) 721-746.
3. G. Bal, Couplage d’équations et homogénéisation en transport neutronique, These de Doctorat de l’Université Paris 6 (1997).
4. G. Bal, Boundary layer analysis in the homogenization of neutron transport equations in a cubic domain. Asymptot. Anal. 20 (1999) 213-239.
5. G. Bal, First-order Corrector for the Homogenization of the Criticality Eigenvalue Problem in the Even Parity Formulation of the Neutron Transport. SIAM J. Math. Anal. 30 (1999) 1208-1240.
6. G. Bal, Diffusion Approximation of Radiative Transfer Equations in a Channel. Transport Theory Statist. Phys. (to appear).
7. P. Benoist, Théorie du coefficient de diffusion des neutrons dans un réseau comportant des cavités, Note CEA-R 2278 (1964).
8. A. Bensoussan, J.L. Lions and G. Papanicolaou, Asymptotic analysis for periodic structures. North-Holland (1978).
9. A. Bensoussan, J.L. Lions and G. Papanicolaou, Boundary Layers and Homogenization of Transport Processes. RIMS, Kyoto Univ. (1979).
10. J. Bergh and L. Lofstrom, Interpolation spaces. Springer, New York (1976).
11. J. Bussac and P. Reuss, Traité de neutronique. Hermann, Paris (1978).
12. Y. Capdeboscq, Homogenization of a diffusion equation with drift. C. R. Acad. Sci. Paris Ser. I Math. 327 (1998) 807-812.
13. Y. Capdeboscq, Homogenization of a Neutronic Critical Diifusion Problem with Drift. Proc. Roy Soc. Edinburgh Sect. A (accepted).
14. F. Chatelin, Spectral approximation of linear operators. Academic Press, Comp. Sci. Appl. Math. (1983).
15. R. Dautray and J.L. Lions, Mathematical analysis and numerical methods for Science and Technology, Vol. 6. Springer Verlag, Berlin (1993).
16. V. Deniz, The theory of neutron leakage in reactor lattices, in Handbook of nuclear reactor calculations, Vol. II, edited by Y. Ronen (1968) 409-508.
17. J. Garnier, Homogenization in a periodic and time dependent potential. SIAM J. Appl. Math. 57 (1997) 95-111.
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.
19. T. Kato, Perturbation theory for linear operators. Springer Verlag, Berlin (1976).
20. M.L. Kleptsyna and A.L. Piatnitski, On large deviation asymptotics for homgenized SDE with a small diffusion. Probab. Theory Appl. (submitted).
21. S. Kozlov, Reductibility of quasiperiodic differential operators and averaging. Trans. Moscow Math. Soc. 2 (1984) 101-136.
22. E.W. Larsen, Neutron transport and diffusion in inhomogeneous media. I. J. Math. Phys. 16 (1975) 1421-1427.
23. E.W. Larsen, Neutron transport and diifusion in inhomogeneous media. II. Nuclear Sci. Engrg. 60 (1976) 357-368.
24. E.W. Larsen and J.B. Keller, Asymptotic solution of neutron transport problems for small mean free paths. J. Math. Phys. 15 (1974) 75-81.
25. E.W. Larsen and M. Williams, Neutron Drift in Heterogeneous Media. Nuclear Sci. Engrg. 65 (1978) 290-302.
26. M. Mokhtar-Kharroubi, Mathematical Topics in Neutron Transport Theory. World Scientific, Singapore (1997).
27. J. Planchard, Méthodes mathématiques en neutronique, Collection de la Direction des Etudes et Recherches d’EDF. Eyrolles (1995).
28. L. Ryzhik, G. Papanicolaou and J.B. Keller, Transport equations for elastic and other waves in random media. Wave Motion 24 (1996) 327-370.
29. R. Sentis, Study of the corrector of the eigenvalue of a transport operator. SIAM J. Math. Anal. 16 (1985) 151-166.
30. M. Struwe, Variational methods: Applications to nonlinear partial differential equations and Hamiltonian systems. Springer, Berlin (1990).