板几何中一类具反射边界条件的奇异迁移方程  

Singular Transport Equations with a Reflecting Boundary Conditions 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）》2007年第6期533-539,544,共8页Journal of Nanchang University(Natural Science)

基　　金：江西省自然科学基金资助项目(0311022)

摘　　要：在L1空间上研究板几何中一类具反射边界条件下各向异性、连续能量、均匀介质的奇异迁移方程,证明了这类方程相应的奇异迁移算子产生C0半群的Dyson-Ph illips展开式的二阶余项R2(是弱紧的,从而得出了该迁移算子的谱在域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 singular transport equations with anisotropic continuous energy homogeneous in slab geometry of reflecting boundary conditions. It proves that the transport operator generates a strongly continuous semigroup and the weak compactness properties of the second - order remained term of the Dys- on - Phillips expansion for the semigroup in space, and to obtain the spectrum of the transport operator only consist of, at most, finitely many isolated eigenvalues which have a finite algebraic multiplicity in trip.

关 键 词：奇异迁移方程 反射边界条件 CO半群 二阶余项 

分 类 号：O177.2[理学—数学]