中文摘要：

运用线性算子理论,研究了板模型中具抽象边界条件的各向异性和连续能量的迁移算子的谱.采用比较算子和豫解算子等方法证明了这类迁移算子产生的C_0半群的Dyson-phillips展开式的第9阶余项的弱紧性,得到了该迁移算子的谱在某区域Γ中仅由有限个具有限代数重数的离散本征值组成.

英文摘要：

First, the objective of this paper is to discuss the spectrum of anisotropic and continuous energy with abstract boundary condition in slab geometry. Second, it is to prove that the transport operator generates a Co semigroup and the ninth-order remained term of the Dyson-phillips expansion of the Co semigroup is weakly compact, and it obtains that the spectrum of the transport operator only consists of finite isolated eigenvalues with a finite algebraic multiplicity in some trip Г. The paper relies on the theory of linear operators, resolvent operator, and comparison operator methods.