Acta mathematica scientia,Series A ›› 2016, Vol. 36 ›› Issue (5): 821-831.

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Spectral Analysis of a Transport Operators in Rotenberg Model

Wang Shenghua, Wu Hongxing   

  1. 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)

Abstract:

The objective of this paper is to research Rotenberg model of a proliferating cell population with unsmooth boundary conditions in Lp(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

CLC Number: 

  • 0177.2
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