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

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.