板几何中迁移半群相应余项的弱紧性  

Weakly compactness of remainder term of transport semigroup in slab geometry

作　　者：袁邓彬[1] 吴红星[1] 王胜华[1] 

机构地区：[1]上饶师范学院数学与计算机科学学院,江西上饶334001

出　　处：《辽宁工程技术大学学报（自然科学版）》2014年第11期1568-1571,共4页Journal of Liaoning Technical University (Natural Science)

基　　金：国家自然科学基金数学天元基金资助项目(11226104);江西省自然科学基金资助项目(20132BA201002);江西省教育厅科技基金资助项目(GJJ13706;GJJ13703)

摘　　要：针对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,L1空间上,证明了奇异迁移算子HA相应的奇异迁移半群V(t)(t≥0)的Dyson-Phillips展开式的n-阶余项Rn(t)(n≥1)的弱紧性,研究结果表明: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HA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.This paper researched the singular transport equations with anisotropic continuous energy homogeneous in slab geometry with a periodic boundary conditions in L1 space, and proved the weakly compactness of the n- order remainder term Rn（t）（n ≥1） of the Dyson-Phillips expansion of transport semigroup V（t）（t≥0） by using the structuring operator and comparing operator. The results of research show 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. consists of countable isolate eigenvalues with finite algebraic mutiplicities in region F and the asymptotic stability of the solution of the transport.

关 键 词：周期边界条件 奇异算子 本质谱 余项 弱紧性 

分 类 号：O177.2[理学—数学]