We study the asymptotic behavior of the principal eigenvalue of a weakly coupled, cooperative linear elliptic system in a stationary ergodic heterogeneous medium. The system arises as the so-called multigroup diffusion model for neutron flux in nuclear reactor cores, the principal eigenvalue determining the criticality of the reactor in a stationary state. Such systems have been well studied in recent years in the periodic setting, and the purpose of this work is to obtain results in random media. Our approach connects the linear eigenvalue problem to a system of quasilinear viscous Hamilton–Jacobi equations. By homogenizing the latter, we characterize the asymptotic behavior of the eigenvalue of the linear problem and exhibit some concentration behavior of the eigenfunctions.
Keywords: Multigroup diffusion model, Stochastic homogenization, Viscous Hamilton–Jacobi system
@article{AIHPC_2013__30_3_419_0,
author = {Armstrong, Scott N. and Souganidis, Panagiotis E.},
title = {Concentration phenomena for neutronic multigroup diffusion in random environments},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {419--439},
year = {2013},
publisher = {Elsevier},
volume = {30},
number = {3},
doi = {10.1016/j.anihpc.2012.09.002},
zbl = {1294.82044},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2012.09.002/}
}
TY - JOUR AU - Armstrong, Scott N. AU - Souganidis, Panagiotis E. TI - Concentration phenomena for neutronic multigroup diffusion in random environments JO - Annales de l'I.H.P. Analyse non linéaire PY - 2013 SP - 419 EP - 439 VL - 30 IS - 3 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2012.09.002/ DO - 10.1016/j.anihpc.2012.09.002 LA - en ID - AIHPC_2013__30_3_419_0 ER -
%0 Journal Article %A Armstrong, Scott N. %A Souganidis, Panagiotis E. %T Concentration phenomena for neutronic multigroup diffusion in random environments %J Annales de l'I.H.P. Analyse non linéaire %D 2013 %P 419-439 %V 30 %N 3 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2012.09.002/ %R 10.1016/j.anihpc.2012.09.002 %G en %F AIHPC_2013__30_3_419_0
Armstrong, Scott N.; Souganidis, Panagiotis E. Concentration phenomena for neutronic multigroup diffusion in random environments. Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 3, pp. 419-439. doi: 10.1016/j.anihpc.2012.09.002
Cité par Sources :