板几何中具广义边界条件的迁移算子的谱  

The Spectrum of the Transport Operator with General 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330031 [2]上饶师范学院数学与计算机系,江西上饶334001

出　　处：《南昌大学学报（理科版）》2009年第5期415-420,共6页Journal of Nanchang University(Natural Science)

基　　金：江西省自然科学基金资助课题(2007GZS0105)

摘　　要：在Lp(1≤p≤∞)空间研究了板几何中具广义边界条件下各向异性、连续能量、非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C0半群的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 nonhomogeneous with general boundary condition in slab geometry. It proves that the transport operator A generates a Co semigroup and the second - order remained term of the Dyson - Phillips expansion for the Co semigroup is compact in L^p （1 〈 p 〈 ∞ ） space and weakly compact in L1 space, and obtains that the spectrum of the transport operator only consists of finite isolated eigenvalues which have a finite algebraic multiplicity in region F.

关 键 词：迁移算子 广义边界条件 C_(0)半群 二阶余项 紧性 本征值 

分 类 号：O173.3[理学—数学]