一类具抽象边界条件的迁移算子的谱分布

The spectrum distribution of a transport operator with abstract boundary condition

利用线性算子半群理论,研究了板几何中具抽象边界条件的各向异性、连续能量、非均匀介质的迁移方程.在假设边界算子H部分光滑和扰动算子K正则的条件下,采用豫解方法,得到了该迁移算子A的谱在区域Γ中由至多可数个具有限代数重数的离散本征值组成等结果.

In this paper, transport operator equation of anisotropic continuous energy nonhomogeneous with abstract boundary condition in slab geometry is studied. Supposing that the H is partly smooth and K is regular, the spectrum of the transport operator A consists of, at most, isolated eigenvalues with finite algebraic multiplicities in the trip F is obtained. The main method relies on theory of semigroups of linear operators and solution method.