Concentration phenomena for neutronic multigroup diffusion in random environments

Abstract

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.