板几何中奇异迁移半群的本质谱

The Essential Spectral of a Singular Transport Semigroup in Slab Geometry

本文在L^p(1<p<+∞)空间上,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、均匀介质的奇异迁移方程.通过构造算子,利用比较算子方法,证明了奇异迁移算子A相应的奇异迁移半群V(t)(t≥0)的Dyson-Phillips展开式的n-阶余项R_n(t)(n≥1)的紧性,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中仅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 objective of this paper is to research singular transport equations with anisotropic continuous energy homogeneous in slab geometry with a periodic boundary conditions in L^p（1P＋∞） space.It proves the compactness of the n-order remainder term R_n（t）（n≥1） of the Dyson-Phillips expansion of 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 A_H consists of countable isolate eigenvalues with finite algebraic multiplicity in trip Γ and the asymptotic stability of the solution to the transport equations.