TY - JOUR
T1 - Concentration phenomena for neutronic multigroup diffusion in random environments
AU - Armstrong, Scott N.
AU - Souganidis, Panagiotis E.
N1 - Funding Information:
The first author was partially supported by NSF Grant DMS-1004645, and the second author by NSF Grant DMS-0901802. We thank Amie Wilkinson and Albert Fathi for helpful comments.
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
KW - Multigroup diffusion model
KW - Stochastic homogenization
KW - Viscous Hamilton-Jacobi system
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U2 - 10.1016/j.anihpc.2012.09.002
DO - 10.1016/j.anihpc.2012.09.002
M3 - Article
AN - SCOPUS:84878520636
SN - 0294-1449
VL - 30
SP - 419
EP - 439
JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
IS - 3
ER -