一类具抽象边界的迁移算子本质谱  

Essential spectrum of a transport operator with abstract boundary conditions

作　　者：吴红星[1] 王胜华[1] 

机构地区：[1]上饶师范学院数学与计算机科学学院,江西上饶334001

出　　处：《辽宁工程技术大学学报（自然科学版）》2014年第1期141-144,共4页Journal of Liaoning Technical University (Natural Science)

基　　金：国家自然科学基金数学天元基金资助项目(11226104);江西省教育厅科技基金资助项目(GJJ13706;GJJ13703)

摘　　要：为得到迁移算子的本质谱的分布情况,在1L空间研究板几何中具抽象边界条件各向异性、连续能量的迁移方程解的渐近性态.采用算子理论和比较算子等方法,在边界算子是部分光滑和扰动算子是正则的条件下,证明了该迁移算子H A产生0C半群的Dyson-Phillps展开式的第九阶余项9R(t)在1L空间中是弱紧算子,从而得到了该迁移算子生成的半群V(t)和streaming算子H B生成的半群U(t)有相同的本质谱半径.In order to obtain the essential spectra of transport operator, the objective of this paper is to discuss the asymptotic behavior of solution to transport equation with anisotropic continuous energy with abstract boundary conditions in slab geometry in L1 space. It is to prove that the transport operator AH generates a CO semigroup and the ninth-order remained term R9 （t） of the Dyson-Phillps expansion of the CO semigroup is weakly compact in L1 space in the conditions of boundary operator being partly compact and disturbance operator is regular, and it to obtain that semigroup V（t） which is generated by the transport operator and semigroup U（t） which is generated by streaming operator BH have the same essential spectral radius. The paper relies on the theory of operators and comparison operator methods, and so on.

关 键 词：迁移方程 抽象边界条件 部分光滑 正则性 比较算子法 余项 紧性 本质谱 

分 类 号：O177.2[理学—数学]