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Rotenberg模型中一类迁移算子的谱分析 被引量：7

Spectral Analysis of a Transport Operators in Rotenberg Model
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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R_9(t)在L_1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. The objective of this paper is to research Rotenberg model of a proliferating cell population with unsmooth boundary conditions in L_p（1p＋∞） space.It is to prove that the ninth-order remainder term R_9（t） of the Dyson-Phillips expansion of corresponding transport operators generates semigroup for this model is compact on L_1 and is weakly compact on（1p＋∞）.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.
作者 王胜华 吴红星
机构地区 上饶师范学院
出处 《数学物理学报（A辑）》 CSCD 北大核心 2016年第5期821-831,共11页 Acta Mathematica Scientia
基金 国家自然科学基金(11461055) 江西省自然科学基金(20151BAB201029)资助~~
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 Cell population Rotenberg＇s model Transport operators Unsmooth boundary conditions Spectral analysis
分类号 O177.2 [理学—基础数学]
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参考文献12

  • 1Lebowitz J L, Rubinow S I. A theory for the age and generation time distribution of a microbial population. J Math Biol, 1974, 1:17-36.
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  • 5王胜华,翁云芳,阳名珠.人体细胞增生中一类迁移算子的谱分析[J].数学物理学报（A辑）,2010,30(4):1055-1061. 被引量：34
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  • 9王胜华,程国飞.一类增生扩散型种群细胞中迁移方程的谱问题[J].数学物理学报（A辑）,2013,33(1):71-77. 被引量：24
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二级参考文献19

  • 1Jeribi A, Megdiche H Moalla N. On a transport arising in growing cell populations II Cauchy problem. Math Methods in the Applied Sciences, 2005, 28:127-145.
  • 2Latrach K, Mokhtar-Kharroubi M. On an unbounded linear operator arising in the theory of growing cell population. J Math Anal Appl, 1997, 211:273-294.
  • 3Boulanouar M. A mathematical study for a Rotenberg model. Math Anal Appl, 2002, 265:371-394.
  • 4Jeribi A. Time asymptotic behaviour for unbounded linear operator arising in growing cell populations. Nonlinear Analysis: Real World Appl, 2003, 4:667-688.
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  • 7Lebowitz J L, Rubinow S I. A theory for the age and generation time distribution of a microbiM population. J Math Biol, 1974, 1:17-36.
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  • 10Latrach K, Mokhtar-Kharroubi M. On an unbounded linear operator arising in the theory of growing cell population. J Math Anal Appl, 1997, 211:273-294.

共引文献41

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数学物理学报（A辑）
2016年 第5期

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