板几何中一类具完全反射边界条件迁移算子的谱  

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

作　　者：袁邓彬[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3期1-4,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(l p<∞)空间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、均匀介质的迁移算子的谱,证明了:这类迁移算子产生C0半群和该半群的Dyson—Phillips展开式的二阶余项在Lp(l<p<∞)空间是紧的及在L空间是弱紧的,并得到了该迁移算子在区域Γ中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 homogeneotts slab geometry in perfect reflecting boundary condition. It proves the transport operator generates a strongly continuovs semigvoup and the compaemess properties of the second- order remained term of the Dyson- Phillips expansion for the semigvoup, and to obtain the spectrum of the transport operator only consist of finite isolated eigenvalue which have a finite algebraic multiplicity in tripГ, and to prove the existence of the dominant eigenvahe.

关 键 词：迁移算子 完全反射边界条件 CO半群 二阶余项 占优本征值 

分 类 号：O177.2[理学—数学]