具广义边界条件及连续能量的中子迁移方程解的渐近性质

Asymptotic behavior of thesolution of the neutron trans port equations with continuative energy and with generalized reflecting boundary conditions

我们在文[9]中给出了具反射边界条件、单能、常系数迁移方程解的稳定性结论。本文是[9]的推广,即给出了具广义边界条件及连续能量、变系数的中子迁移方程解的稳定性理论,为此,先分析了迁移算子的谱性质:进而又证明了迁移算子至少存在一个实体征质,事实上其就是占优本征值;最后给出了t(?)∞时中子密度的渐近性质及在Hileert空间L_2(X)内中子分布的渐近表示。

In this paper, we give the stability theory of the solution of the neutron transport eguations with continuative enevgy and with generalized reflecting boundary conditions. In order to do this, first, we analyze spectrum of transpert Operator and prove the existence and the uniqueness of the positive solution of the system given in the Papev. Moreover, we show that the transport operator has at least one real eigenvalue, in fact, which is the dominate eigenvalue. At last, we can indicate the asymptotic behavior of the neutron density ast→∞ and the asymptotic represent of the neutron distribution in the Hilbert space L_2(X).