板几何中具完全反射边界条件的迁移方程  

Transport Equation with Perfect Reflecting Boundary Condition in Slab Geometry

作　　者：王胜华[1] 张传美[2] 

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

出　　处：《上饶师范学院学报》2008年第6期1-5,共5页Journal of Shangrao Normal University

基　　金：江西省自然科学基金资助课题(2007GZS0105)

摘　　要：在Lp(1≤p<∞)空间上研究了板几何中具完全反射边界条件下各向异性、连续能量、非均匀介质的迁移方程,证明了该迁移算子产生C0群和该群的Dyson-Phillips展开式的二阶余项在Lp(1<p<∞)空间上是紧的和在L1空间上弱紧的,从而得到了该迁移算子的谱在区域Γ中仅由有限个具有限代数重数的离散本征值组成和占优本征值的存在性等结果。The objective of tiffs paper is to research spectral analysis of transport operator with anisotropic continuous energy nonho- niogeneous slab gemetry in perfect reflecting boundary condition, it proves thet the ransport operator generates a Co group and the second-order renmined term of the Dyson-phillips espansion for the Co group are compact in LP（ 1 〈 p 〈 ∞ ） space and weakly com- pact in Ll space, and obtains the spectrum of the transport operator only consist of finite isolated eigenvalue which have a finite algebraic multiplicity in trip Г and the existence of the dominand eigenvalue.

关 键 词：迁移方程 完全反射边界条件 二阶余项 紧性 占优本征值 

分 类 号：O177.2[理学—数学]