板几何中具反射边界条件的迁移算子的谱分析  

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

作　　者：王胜华 吴红星[2] 

机构地区：[1]上饶师院数学与计算机系,上饶334000 [2]南昌大学数学系,南昌330047

出　　处：《数学的实践与认识》2008年第22期197-203,共7页Mathematics in Practice and Theory

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半群的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 this paper is to research spectral analysis of transport operator with anisotropic continuous energy nonhomogeneous slab geometry in reflecting boundary condition. it proves the transport operator generates a Co semigroup and the second-order remained term of the Dyson-Phillips expansion for the C0 semigroup is compact in L^P（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, and to prove the existence of the dominand eigenvalue.

关 键 词：迁移方程 反射边界条件 二阶余项 紧性 占优本征值 

分 类 号：O177[理学—数学]