板几何中一类具广义边界条件的奇异迁移算子的谱  

The Spectrum of a Singular Transport Operator with Generalized Boundary Conditions in Slab Geometry

作　　者：王胜华[1] 张传美[2] 

机构地区：[1]上饶师范学院数学与计算机系,江西上饶334001 [2]南昌大学数学系,江西南昌330031

出　　处：《南昌大学学报（理科版）》2008年第6期535-539,共5页Journal of Nanchang University(Natural Science)

基　　金：江西省自然科学基金资助项目(2007GZS0105)

摘　　要：在Lp空间上研究板几何中一类具广义边界条件下各向异性、连续能量、均匀介质的奇异迁移方程。证明了其相应的奇异迁移算子产生C0半群和该半群的Dyson-Phillips展式的二阶余项是紧的,且该算子的谱在区域Γ中由至多可数个具有限重的离散本征值组成等结果。The objective of this paper is to research singular transport equations with anisotropic continuous energy homogeneous slab geometry for generalized boundary condition in slab geometry. It proves that the transport operator generates a strongly continuous C0 semigroup V（t） （ t≥0） and the compactness properties of the second - order remaineder term of the Dyson -Phillips expansion for the C0 semigroup V（t） （t ≥0） in L^P（ 1 〈p 〈 ∞） space. It obtains the spectrum of the transport operator consist of at most,isolate eigenvalues which have a finite algebraic multi- plicity in trip Г.

关 键 词：奇异迁移方程 广义边界条件 C0半群 二阶余项 

分 类 号：O175[理学—数学]