摘要
在L1空间中,利用算子理论、半群理论探讨了具抽象边界条件的非均匀介质的中子迁移算子的谱分布情况。在考虑扰动算子是正则的和边界算子是部分光滑的条件下,运用豫解算子等方法,论证了相应的迁移算子所生成的C0半群所产生的余项R9(t)在L1空间中的弱紧性,获得了该算子的点谱集仅由有限个具有限代数重数的离散本征值构成。
The objective of this paper is to research the transport equation of continuous energy and inhomogeneous medium with abstract boundary conditions in L1 space. It is to prove that the transport operator generates C0 semigroup and the remained term R9 （t） of the Dyson-Phillips expansion of the semigroup is weakly compact in L1 space with the boundary operator being partly compact and disturbance operator is regular, and it obtains that the spectrum of the transport operator only consists of finite isolated eigenvalues with finite algebraic multiplicity. The main metheods rely on the theory of linear operators, resolvent and comparison operator.
出处
《上饶师范学院学报》
2016年第3期1-5,共5页
Journal of Shangrao Normal University
基金
国家自然科学基金(11461055)
江西省自然科学基金(20151BAB201029)
江西省教育厅科技项目(151056)
关键词
抽象边界条件
紧性
迁移方程
正则性
离散本征值
abstract boundary condition
compactness
transport equation
regularity
discrete eigenvalues
