Rotenberg模型中一类迁移算子的谱分析

数学物理学报 ›› 2016, Vol. 36 ›› Issue (5): 821-831.

Rotenberg模型中一类迁移算子的谱分析

王胜华, 吴红星

上饶师范学院江西上饶 334001

收稿日期:2015-11-17 修回日期:2016-04-25 出版日期:2016-10-26 发布日期:2016-10-26
作者简介:王胜华,E-mail:wshua@sru.jx.cn
基金资助:
国家自然科学基金（11461055）和江西省自然科学基金（20151BAB201029）资助

Spectral Analysis of a Transport Operators in Rotenberg Model

Wang Shenghua, Wu Hongxing

Shangrao Normal University, Jiangxi Shangrao 334001

Received:2015-11-17 Revised:2016-04-25 Online:2016-10-26 Published:2016-10-26
Supported by:
Supported by the NSFC (11461055) and the Natural Science Foundation of Jiangxi Province (20151BAB201029)

摘要/Abstract

摘要：

该文在L_p(1 ≤p <+∞)空间上，研究了种群细胞增生中一类具非光滑边界条件的Rotenberg模型，证明了这类模型相应的迁移算子生成半群的Dyson-phillips展式的9阶余项R₉(t)在L₁空间上是弱紧和在L_p(1 <p <+∞)空间上是紧的，从而获得了该迁移算子的谱在某右半平面上仅由有限个具有限代数重数的离散本征值组成及该迁移方程解的渐近稳定性等结果.

关键词: 种群细胞, Rotenberg模型, 非光滑边界条件, 9阶余项的紧性, 谱分析

Abstract:

The objective of this paper is to research Rotenberg model of a proliferating cell population with unsmooth boundary conditions in L_p(1 ≤p <+∞) space. It is to prove that the ninth-order remainder term R₉(t) of the Dyson-Phillips expansion of corresponding transport operators generates semigroup for this model is compact on L₁ and is weakly compact on (1 <p <+∞). It is to obtain that the spectrum of the transport operators only consisting of finitely isolate eigenvalues with finite algebraic multiplicities in the right half plane and the stability of the transport equation solution and so on.

Key words: Cell population, Rotenberg's model, Transport operators, Unsmooth boundary conditions, Spectral analysis

中图分类号:

0177.2

王胜华, 吴红星. Rotenberg模型中一类迁移算子的谱分析[J]. 数学物理学报, 2016, 36(5): 821-831.

Wang Shenghua, Wu Hongxing. Spectral Analysis of a Transport Operators in Rotenberg Model[J]. Acta mathematica scientia,Series A, 2016, 36(5): 821-831.

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