板几何中奇异迁移方程解的渐近稳定性  

The Asymptotic Stability of the Solution to the Singular Transport Equations In Slab Geometry

作　　者：袁邓彬[1] 程国飞[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

出　　处：《数学的实践与认识》2014年第10期235-242,共8页Mathematics in Practice and Theory

基　　金：江西省自然科学基金资助课题(20132BAB201002);江西省教育厅资助课题(GJJ13706)

摘　　要：在L^p(1<p<+∞)空间,研究了板几何中一类具反射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展开式的一阶余项R_1(t)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T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 objective of this paper is to research singular transport equations with anisotropic continuous energy homogeneous in slab geometry of reflecting boundary conditions in L^p（1 p ＋∞）.It proves the compactness of the first order remainder term R1（t）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 Ah consists of finite isolate eigenvalues with finite algebraic multiplicity in trip Γ and the asymptotic stability of the solution of the transport equations.

关 键 词：反射边界条件 奇异算子 本质谱 奇异迁移方程 

分 类 号：O175[理学—数学]