板几何中一类具完全反射边界条件的奇异迁移算子的谱

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

在L1空间上研究了板几何中一类具完全反射边界条件下各向异性、连续能量、均匀介质的奇异迁移方程.证明了这类方程相应的奇异迁移算子产生C0半群和该半群的Dyson-Phillips展开式的二阶余项是弱紧的,从而得到了该迁移算子的谱在区域Γ中仅由至多有限个具有限代数重数的离散本征值组成等结果.

The objective of this paper is to research singular transport equations with anisotropic continuous energy homogeneous slab geometry for perfect reflecting boundary condition in slab geometry. It proves the singular transport operator generates a strongly continuous Co semigroup V（t） （t≥0） and the weak compactness properties of the second-order remained term of the Dyson- Phillips expansion for the Co semigroup V（t）（t≥0） in L^1 space, and to obtain the spectrum of the singular transport operator only consist of, at most, finitely many isolate eigenvalues which have a finite algebraic multiplicity in trip Г.