随机环境中中子多群扩散的浓集现象
Concentration phenomena for neutronic multigroup diffusion in random environments
摘要：
研究了平稳各态历经非均匀介质中弱耦合合作线性椭圆方程组主特征值的渐近性态。该系统作为核反应堆堆芯中子通量的所谓多群扩散模型而出现，该模型的主要特征值确定了稳态下反应堆的临界性。这类系统近年来在周期环境中得到了很好的研究，这项工作的目的是在随机介质中获得结果。我们的方法连接的线性本征值问题的拟线性粘性Hamilton-Jacobi方程组。通过对后者的研究，我们刻画了线性问题特征值的渐近性态，并展示了特征函数的某些集中性态。
英文摘要：
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.
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