Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (3): 807-817.

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Asymptotic Stability Analysis of Solutions to Transport Equations in Structured Bacterial Population Growth

Hongxing Wu*(),Dengbin Yuan,Shenghua Wang   

  1. Shangrao Normal University, Jiangxi Shangrao 334001
  • Received:2019-08-27 Online:2022-06-26 Published:2022-05-09
  • Contact: Hongxing Wu
  • Supported by:
    the NSFC(11861053);the NSFC(11461055);the Science and Technology Project of Education Department of Jiangxi Province(GJJ201714);the Science and Technology Project of Shangrao City(2020L007)


With the help of linear operator theory, the transport equation with more general boundary condition for the structured equation with bacterial population as background is discussed. By means of resolving operator and comparison operator, it is proved that the corresponding transfer operator spectrum of the transfer equation consists of only a finite number of discrete eigenvalues with finite algebraic multiplicity in band domain $\Gamma_{\alpha, \beta}$. It is proved that the solution of the transfer equation is asymptotically stable when $\psi_0 \in D (A_{H_{\alpha, \beta}})$.

Key words: Bacterial population, Transport equation, Discrete eigenvalues, Asymptotic stability

CLC Number: 

  • O177.2