板几何中一类具周期边界条件的奇异迁移算子的谱

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

在Lp(1<p<∞)空间上研究了板几何中一类具周期边界条件下各向异性、连续能量、均匀介质的奇异迁移方程,证明了其相应的奇异迁移算子产生C0半群和该C0半群的Dyson-Phillips展开式的二阶余项是紧的,从而该算子的谱在区域Γ中由具有限重的离散本征值组成等结果.

This paper is to research singular transport equations with anisotropic continuous energy homogeneous slab geometry for periodic boundary condition in slab geometry. It proves the transport operator generates a strongly continuous Co semigroup and the compactness properties of the second-order remained term of the Dyson-Phillips expansion for the Co semigroup in L^p （1〈 p 〈∞） space ,and to obtain the spectrum of the transport operator consist of isolate eigenvalues which have a finite algebraic multiplicity in trip Г .