周期边界条件的一般奇异迁移算子的谱分析

在L^p（1〈P〈∞）空间上研究了板几何中具周期边界条件下各向异性、连续能量、非均匀介质的奇异迁移方程,证明了其相应的奇异迁移算子A产生C0半群V（t）（t≥0）和该半群的Dyson-Phillips展开式的二阶余项是紧的,并得到了该奇异迁移算子的谱在区域Г中仅由有限个具有限代数重数的离散本征值组成等结果.

Spectral Analysis of the General Singular Transport Operator with Periodic Boundary Conditions

This paper researches the general singular transport equations in Lp（1p∞） space for anisotropic,continuous energy,nonhomogeneous with periodic boundary conditions in slab geometry. It proves that the transport operator A generates a strongly continuous C0 semigroup V（t）（t≥0） and the compactness of the second-order remained term of the D yson-Phillips expansion for the C0 semigroup V（t）（t≥0）,and it obtains the results that the spectrum of the transport operator only consist of finitely many isolate eigenvalues which have a finite algebraic multiplicity in tripΓ.