板几何中具反射边界条件的迁移算子的谱

The Spectrum of Transport Operator with Reflecting Boundary Condition in Slab Geometry

在LP(1p<∞)空间研究了板几何中一类带反射边界条件具各向异性、连续能量、均匀介质迁移算子的谱,证明了该迁移算子生成C0半群的Dyson-Phillips展开式的二阶余项在LP(1<P<∞)(L1)空间中是紧(弱紧)的,从而得到了该迁移算子的占优本征值的存在性等结果.

The objective of this paper is to research spectral analyse of transport operator with anisotropic continuous energy homogeneous slab geometry in reflecting boundary condition, it proves the transport operator generates a strongly continuous semigroup and the compactness properties of the second-order remained term of the Dyson-Phillips expansion for the Co semigroup, and to obtain the spectrum of the transport operator only consist of finite isolated eigenvalue which have a finite algebraic multiplicity in trip Г, and to prove the existence of the dominand eigenvalue .