一般迁移方程相应余项的弱紧性及其应用

在L¹空间,研究了板几何中一类具周期边界条件的各向异性、连续能量、均匀介质的迁移方程.通过构造算子,利用比较算子方法,证明了该迁移算子A相应的迁移半群V(t)(t≥0)的Dyson-Phillips展开式的伽阶余项R_n(t)(n≥1)的弱紧性,得到了半群V(t)与U(t)(streaming算子B产生)本质谱相同,本质谱型一致;迁移算子A的谱在区域Γ中由有限个具有限代数重数的离散本征值组成;迁移方程解的渐近稳定性.

The Weakly Compactness and the Application of Remainder Term to the Transport Equation

It researches the transport equations with anisotropic continuous energy homogeneous in slab geometry with a periodic boundary conditions in L~1 space.It proves the weakly compactness of the n-order remainder term R_n(t)(n ≥ 1) of the Dyson-Phillips expansion of the transport semigroup V(t)(t ≥ 0) by using the structuring operator,comparing operator.In the last,it obtains that the semigroup V(t) and semigroup U(t)(generated by the streaming operator B)have the same essential spectral,the same type of the essential spectral;the spectrum of the transport operators Ah consists of countable isolate eigenvalues with finite algebraic multiplicity in trip Γ and the asymptotic stability of the solution to the transport equations.