板几何中一类具周期边界条件迁移算子的谱

The Spectrum of Transport Operator with a Periodic Boundary Conditions in Slab Geometry

研究板几何中一类具周期边界条件下具各向异性、连续能量、均匀介质的迁移算子的谱分析．证明了这类迁移算子产生C0群和该群的Dyson-Phillips展开式的二阶余项是紧的,从而得到了该迁移算子的谱在区域Γ中仅由有限个具有限代数重数的离散本征值组成和占优本征值的存在性等结果．

The objective of this paper is to research spectral analysis of transport operator with anisotropic continuous energy homogeneous slab geometry in periodic boundary condition. It proves the transport operator generates a strongly continuous group and the compactness properties of the second-order remained term of the Dyson-Phillips expansion for the C0 group, and to obtain the spectrum of the transport operator only consist of finite isolated eigenvalue which has a finite algebraic multiplicity in trip Γ, and to prove the existence of the dominant eigenvalue.