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具扰动项的L-R型迁移算子的谱分析

王胜华,贾善德,黄时祥   

  1. 饶师范学院,上饶 334001
  • 收稿日期:2013-10-08 出版日期:2014-04-25 发布日期:2014-07-18

王胜华,贾善德,黄时祥. 具扰动项的L-R型迁移算子的谱分析[J]. 系统科学与数学, 2014, 34(4): 443-451.

WANG Shenghua, JIA Shande, HUANG Shixiang. SPECTRAL ANALYSIS OF TRANSPORT OPERATORS IN L-R MODEL WITH PERTURBATION TERM[J]. Journal of Systems Science and Mathematical Sciences, 2014, 34(4): 443-451.

SPECTRAL ANALYSIS OF TRANSPORT OPERATORS IN L-R MODEL WITH PERTURBATION TERM

WANG Shenghua, JIA Shande, HUANG Shixiang   

  1. Shangrao Normal University, Shangrao 334001
  • Received:2013-10-08 Online:2014-04-25 Published:2014-07-18
在$L_{p}(1\leq p<+\infty)$空间上,研究了种群细胞增生中一类具扰动项非光滑边界条件的L-R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$L_{p}(1<p<+\infty)$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行为等结果.
This paper deals with the L-R model with perturbation term of cell pop-ulations with unsmooth boundary conditions in Lp space (1 ≤ p < +∞). It is proven
that the ninth-order remainder term R9(t) of the Dyson-Phillips expansion of cor-responding transport operators generates semigroup for this model which is weakly compact on L1 and is compact on Lp(1 < p < +∞), and that the spectrum of the transport operators only consist of finitely isolate eigenvalues with finite algebraic multiplicities in the right half plane. Finally, the asymptotic behavior of the transport equation solution is given.

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[1] 吴红星,王胜华,袁邓彬. 种群细胞增生中迁移算子的谱研究[J]. 系统科学与数学, 2017, 37(3): 940-949.
[2] 王胜华,马江山,贾善德. 具扰动项的L-R模型迁移方程解的渐近行为[J]. 系统科学与数学, 2017, 37(1): 313-320.
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