板几何中最一般的奇异迁移算子的谱分析  

The Spectrum of the General Singular Transport Equations in Slab Geometry

作　　者：袁邓彬[1] 张传美[2] 吴红星[1] 

机构地区：[1]上饶师范学院,江西上饶334001 [2]南昌大学数学系,江西南昌330047

出　　处：《上饶师范学院学报》2009年第6期11-16,共6页Journal of Shangrao Normal University

基　　金：江西省自然科学基金资助课题(2007GZS0105);江西省高校重点学科经费资助

摘　　要：本文研究了板几何中具完全反射边界条件的各向异性、连续能量、非均匀介质的奇异迁移方程,讨论了奇异迁移算子A产生C0半群V(t)(t≥0),并证明了该半群的Dyson-Phillips展开式的二阶余项的弱紧性和迁移算子A的本征值的存在性,从而得到了该算子A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等结果。This paper researches the singular transport equations for anisotropie, continuous energy, nonhomogeneous media with perfectly reflecting boundary conditions in slab geometry. It also discuses that the transport operator generates a strongly continuous semigroup . In addition, it proves the weak compactness of the second- order remainer term of the Dysofi- Phillips expansion and the existence of a eigenvalue of the transport operator, so it obtains the results that the spectrum of the transport operator only consist offinitely many isolate eigenvalues which have a finite algebraiemuhiplieity in trip.

关 键 词：奇异迁移方程 二阶余项 弱紧性 

分 类 号：O177.2[理学—数学]