摘要
The spectrum of neutron transport operator A in an arbitrary non-homogeneous slab geometry is discussed in consideration of anisotropic scatteringand fission.Under the assumptions that the boundary reflection coefficient func-tion α（v,μ）,γ（v,μ）and the scattering-fission kernel k（x,v,v′,μ,μ′）are boundedmeasurable,and the total collision frequency v∑（x,v）is square integrable,it isshown that A has at most finite spectrum points in any strip{λ=β+i（?）|β<sub>1</sub>（?）β（?）β<sub>2</sub>},where β<sub>2</sub>】β<sub>1</sub>】-λ<sup>*</sup>,with λ<sup>*</sup> the essential infimum of v∑（x,v）.Fi-nally,the asymptotic expansion of the solution for the time-dependent equation（dN）/（dt）=AN,N（0）=N<sub>0</sub> is given as a corollary.
The spectrum of neutron transport operator A in an arbitrary non-homogeneous slab geometry is discussed in consideration of anisotropic scatteringand fission.Under the assumptions that the boundary reflection coefficient func-tion α(v,μ),γ(v,μ)and the scattering-fission kernel k(x,v,v′,μ,μ′)are boundedmeasurable,and the total collision frequency v∑(x,v)is square integrable,it isshown that A has at most finite spectrum points in any strip{λ=β+i(?)|β_1(?)β(?)β_2},where β_2>β_1>-λ~*,with λ~* the essential infimum of v∑(x,v).Fi-nally,the asymptotic expansion of the solution for the time-dependent equation(dN)/(dt)=AN,N(0)=N_0 is given as a corollary.
基金
Project supported by the National Natural Science Foundation of China
