板模型中一类具抽象边界条件的迁移方程解的渐近稳定性  

The Stability of a Transport Equations Solution with Abstract Boundary Condition in Slab Geometry

作　　者：吴红星[1] 王胜华[1] 程国飞[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：《数学物理学报（A辑）》2016年第4期703-714,共12页Acta Mathematica Scientia

基　　金：国家自然科学基金(11461055;11561057);江西省自然科学基金(20151BAB201029);江西省教育厅科技项目(151056)资助~~

摘　　要：运用线性算子理论,研究了板模型中一类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.采用半群理论、比较算子和豫解算子等方法证明了相应的迁移算子产生的C_0半群的Dyson-phillips展开式的第九阶余项的弱紧性,得到了这类迁移算子的谱在区域Γ_0中仅由有限个具有限代数重数的离散本征值组成.最后讨论了该迁移方程解的渐近稳定性.First, the objective of this paper is to discuss the transport equation of anisotropic, continuous energy and inhomogeneous medium with abstract boundary condition in slab geometry. Second, it is to prove that the transport operator generates a C0 semigroup and the ninth-order remained term of the Dyson-phillips expansion of the C0 semigroup is weakly compact, and it obtains that the spectrum of the transport operator only consists of finite isolated eigenvalues with a finite algebraic multiplicity in the trip Γ0. Finally, it discusses the solution of transport equation is asymptotic stability. The paper relies on the theory of linear operators, resolvent operator, and comparison operator methods.

关 键 词：迁移方程 抽象边界条件 弱紧算子 离散本征值 稳定性 

分 类 号：O177.2[理学—数学]