周期边界条件的一般奇异迁移算子的谱分析  

Spectral Analysis of the General Singular Transport Operator with Periodic Boundary Conditions

作　　者：王胜华[1] 袁邓彬[1] 

机构地区：[1]上饶师范学院数学与计算机系,上饶334001

出　　处：《应用泛函分析学报》2010年第3期239-244,共6页Acta Analysis Functionalis Applicata

基　　金：江西省自然科学基金(2007GZS0105)

摘　　要：在L^p(1<P<∞)空间上研究了板几何中具周期边界条件下各向异性、连续能量、非均匀介质的奇异迁移方程,证明了其相应的奇异迁移算子A产生C_0半群V(t)(t≥0)和该半群的Dyson-Phillips展开式的二阶余项是紧的,并得到了该奇异迁移算子的谱在区域■中仅由有限个具有限代数重数的离散本征值组成等结果.This paper researches the general singular transport equations in Lp（1p∞） space for anisotropic,continuous energy,nonhomogeneous with periodic boundary conditions in slab geometry. It proves that the transport operator A generates a strongly continuous C0 semigroup V（t）（t≥0） and the compactness of the second-order remained term of the D yson-Phillips expansion for the C0 semigroup V（t）（t≥0）,and it obtains the results that the spectrum of the transport operator only consist of finitely many isolate eigenvalues which have a finite algebraic multiplicity in tripΓ.

关 键 词：奇异迁移方程 周期边界条件 二阶余项 紧性 离散本征值 

分 类 号：O177.2[理学—数学]