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

数学物理学报 ›› 2016, Vol. 36 ›› Issue (4): 703-714.

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

吴红星, 王胜华, 程国飞

上饶师范学院数学与计算机科学学院江西上饶 334001

收稿日期:2015-12-11 修回日期:2016-05-12 出版日期:2016-08-26 发布日期:2016-08-26
通讯作者: 王胜华 E-mail:jxsruwsh@163.com
作者简介:吴红星,jxsruwhx@163.com
基金资助:
国家自然科学基金（11461055，11561057）、江西省自然科学基金（20151BAB201029）和江西省教育厅科技项目（151056）资助

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

Wu Hongxing, Wang Shenghua, Cheng Guofei

College of Mathematics and Computer Science, Shangrao Normal University, Jiangxi Shangrao 334001

Received:2015-12-11 Revised:2016-05-12 Online:2016-08-26 Published:2016-08-26
Supported by:
Supported by the NSFC(11461055,11561057),the Natural Science Foundation of Jiangxi Province(20151BAB201029) and the Science and Technology Project of Education Department of Jiangxi Province(151056)

摘要/Abstract

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C₀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Γ₀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.

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

Abstract:

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.

Key words: Transport equation, Abstract boundary condition, Weakly compactness, Discrete eigenvalues, Stability

中图分类号:

O177.2

吴红星, 王胜华, 程国飞. 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[J]. 数学物理学报, 2016, 36(4): 703-714.

Wu Hongxing, Wang Shenghua, Cheng Guofei. The Stability of a Transport Equations Solution with Abstract Boundary Condition in Slab Geometry[J]. Acta mathematica scientia,Series A, 2016, 36(4): 703-714.

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