板几何中一类具反射边界条件的奇异迁移算子的谱

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

在Lp(1<p<∞)空间上研究板几何中一类具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.证明其奇异迁移算子产生C0半群和该半群的Dyson-Phillips展开式的二阶余项是紧的,且得到了该算子的谱在区域Γ中由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 a reflecting boundary condition in Lp space. It proves the singular transport operator generates a strongly continuous Co semigroup V（t）（t ≥0） and the compactness properties of the second-order remained term of the Dyson-Phillips expansion for the Co semigroup V（t）（t ≥0） in Lp space, and to obtain the spectrum of the transport operator consist of isolate eigenvalues which have a finite algebraic multiplicity in trip Г.