板模型中具周期边界条件迁移算子的谱分析  

The Spectral Analysis of the Transport Operator with Periodic Boundary Condition in Slab Geometry

作　　者：吴红星[1] 王胜华[2] 

机构地区：[1]南昌大学数学系,江西南昌330047 [2]上饶师范学院,江西上饶334001

出　　处：《上饶师范学院学报》2006年第6期1-3,7,共4页Journal of Shangrao Normal University

基　　金：江西省自然科学基金资助课题(0311022)

摘　　要：在Lp(1 p<∞)空间研究了板模型中具周期边界条件下各向异性、连续能量、均匀介质的迁移算子的谱,证明了:这类迁移算子产生C0群的Dyson—Phillips展开式的二阶余项在Lp(1<p<∞)空间是紧的及在L1空间是弱紧的,并得到了该迁移算子在区域Γ中仅由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 spectral analysis of transport operator with anisotropic continuous energy homogeneous with periodic boundary condition in slab geometry. It proves the transport operator generates a C0 group and the second-order remained term of the Dyson- Phillips expansion for the C0 group is compact in Lp （ 1 〈 p 〈∞ ） space and Weakly compact in L^1 space, and to obtain the spectrum of the transport operator only consist of finite isolated eigenvalue which have a finite algebraic multiplicity in trip Г.

关 键 词：迁移算子 周期边界条件 C0群 二阶余项 紧性 本征值 

分 类 号：O177.2[理学—数学]