Concentration phenomena for neutronic multigroup diffusion in random environments

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 30, Issue 3, 2013, Pages 419-439

  Armstrong, Scott N ^a   Souganidis, Panagiotis E ^b  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

Multigroup diffusion model; Stochastic homogenization; Viscous Hamilton Jacobi system

Indexed keywords

ASYMPTOTIC ANALYSIS; DIFFUSION; STOCHASTIC MODELS;

ASYMPTOTIC BEHAVIORS; CONCENTRATION PHENOMENA; DIFFUSION MODEL; HAMILTON JACOBI EQUATIONS; HAMILTON-JACOBI; HETEROGENEOUS MEDIUM; PRINCIPAL EIGENVALUES; STOCHASTIC HOMOGENIZATION;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 84878520636     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpc.2012.09.002     Document Type: Article

References (38)

1. M.A. Akcoglu, and U. Krengel Ergodic theorems for superadditive processes J. Reine Angew. Math. 323 1981 53 67
2. G. Allaire, and G. Bal Homogénéisation dune équation spectrale du transport neutronique C. R. Acad. Sci. Paris Sér. I Math. 325 9 1997 1043 1048
3. G. Allaire, and G. Bal Homogenization of the criticality spectral equation in neutron transport M2AN Math. Model. Numer. Anal. 33 4 1999 721 746
4. G. Allaire, and Y. Capdeboscq Homogenization of a spectral problem in neutronic multigroup diffusion Comput. Methods Appl. Mech. Engrg. 187 1-2 2000 91 117
5. G. Allaire, Y. Capdeboscq, and A. Piatnitski Homogenization and localization with an interface Indiana Univ. Math. J. 52 6 2003 1413 1446
6. G. Allaire, Y. Capdeboscq, A. Piatnitski, V. Siess, and M. Vanninathan Homogenization of periodic systems with large potentials Arch. Ration. Mech. Anal. 174 2 2004 179 220
7. G. Allaire, and F. Malige Analyse asymptotique spectrale dun problème de diffusion neutronique C. R. Acad. Sci. Paris Sér. I Math. 324 8 1997 939 944
8. G. Allaire, and R. Orive Homogenization of periodic non self-adjoint problems with large drift and potential ESAIM Control Optim. Calc. Var. 13 4 2007 735 749 (electronic)
9. G. Allaire, I. Pankratova, and A. Piatnitski Homogenization and concentration for a diffusion equation with large convection in a bounded domain J. Funct. Anal. 262 2012 300 330
10. G. Allaire, and A. Piatnitski Uniform spectral asymptotics for singularly perturbed locally periodic operators Comm. Partial Differential Equations 27 3-4 2002 705 725
11. L. Ambrosio, and H. Frid Multiscale Young measures in almost periodic homogenization and applications Arch. Ration. Mech. Anal. 192 1 2009 37 85
12. S.N. Armstrong, and P.E. Souganidis Stochastic homogenization of Hamilton-Jacobi and degenerate Bellman equations in unbounded environments J. Math. Pures Appl. 97 2012 460 504
13. M.E. Becker Multiparameter groups of measure-preserving transformations: A simple proof of Wieners ergodic theorem Ann. Probab. 9 3 1981 504 509
14. J. Busca, and B. Sirakov Harnack type estimates for nonlinear elliptic systems and applications Ann. Inst. H. Poincaré Anal. Non Linéaire 21 5 2004 543 590
15. Y. Capdeboscq Homogenization of a diffusion equation with drift C. R. Acad. Sci. Paris Sér. I Math. 327 9 1998 807 812
16. Y. Capdeboscq Homogenization of a neutronic critical diffusion problem with drift Proc. Roy. Soc. Edinburgh Sect. A 132 3 2002 567 594
17. M.G. Crandall, H. Ishii, and P.-L. Lions Users guide to viscosity solutions of second order partial differential equations Bull. Amer. Math. Soc. (N.S.) 27 1 1992 1 67
18. V. Deniz The theory of neutron leakage in reactor lattices Y. Ronen, Handbook of Nuclear Reactor Calculations, vol. II 1986 Chemical Rubber Company Boca Raton 409 508
19. L.C. Evans The perturbed test function method for viscosity solutions of nonlinear PDE Proc. Roy. Soc. Edinburgh Sect. A 111 3-4 1989 359 375
20. H. Ishii On the equivalence of two notions of weak solutions, viscosity solutions and distribution solutions Funkcial. Ekvac. 38 1 1995 101 120
21. H. Ishii Almost periodic homogenization of Hamilton-Jacobi equations International Conference on Differential Equations, vols. 1, 2 Berlin, 1999 2000 World Sci. Publ. River Edge, NJ 600 605
22. H. Ishii, and S. Koike Viscosity solutions for monotone systems of second-order elliptic PDEs Comm. Partial Differential Equations 16 6-7 1991 1095 1128
23. E. Kosygina, F. Rezakhanlou, and S.R.S. Varadhan Stochastic homogenization of Hamilton-Jacobi-Bellman equations Comm. Pure Appl. Math. 59 10 2006 1489 1521
24. S.M. Kozlov The averaging method and walks in inhomogeneous environments Uspekhi Mat. Nauk 40 2(242) 1985 61 120 238
25. N.V. Krylov Nonlinear Elliptic and Parabolic Equations of the Second Order Mathematics and Its Applications (Soviet Series) vol. 7 1987 D. Reidel Publishing Co. Dordrecht translated from the Russian by P.L. Buzytsky [P.L. BuzytskiÄ]
26. E.W. Larsen Neutron transport and diffusion in inhomogeneous media. I J. Math. Phys. 16 1975 1421 1427
27. E.W. Larsen Neutron transport and diffusion in inhomogeneous media Nucl. Sci. Eng. 60 1976 357 368
28. E.W. Larsen, and M. Williams Neutron drift in heterogeneous media Nucl. Sci. Eng. 65 1978 290 302
29. P.-L. Lions, and P.E. Souganidis Correctors for the homogenization of Hamilton-Jacobi equations in the stationary ergodic setting Comm. Pure Appl. Math. 56 10 2003 1501 1524
30. P.-L. Lions, and P.E. Souganidis Homogenization of "viscous" Hamilton-Jacobi equations in stationary ergodic media Comm. Partial Differential Equations 30 1-3 2005 335 375
31. P.-L. Lions, and P.E. Souganidis Stochastic homogenization of Hamilton-Jacobi and "viscous"-Hamilton-Jacobi equations with convex nonlinearities - Revisited Commun. Math. Sci. 8 2 2010 627 637
32. E. Mitidieri, and G. Sweers Weakly coupled elliptic systems and positivity Math. Nachr. 173 1995 259 286
33. B. Perthame, and P.E. Souganidis Asymmetric potentials and motor effect: A homogenization approach Ann. Inst. H. Poincaré Anal. Non Linéaire 26 6 2009 2055 2071
34. A.L. Piatnitski Asymptotic behaviour of the ground state of singularly perturbed elliptic equations Comm. Math. Phys. 197 3 1998 527 551
35. Rn Tr. Semin. im. I.G. Petrovskogo 23 2003 287 308 412
36. G. Sweers Strong positivity in C (Ω ̄) for elliptic systems Math. Z. 209 2 1992 251 271
37. A.M. Weinberg, and E.P. Wigner The Physical Theory of Neutron Chain Reactors 1958 The University of Chicago Press
38. A. Wilkinson, personal communication.