Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (5): 1320-1331.

Previous Articles     Next Articles

Spectral Analysis of the Main Operator of Rotenberg Equation with Time Delay Under Nonsmooth Boundary Conditions

Yage Tong(),Kaisu Wu*()   

  1. School of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029
  • Received:2021-08-12 Online:2022-10-26 Published:2022-09-30
  • Contact: Kaisu Wu E-mail:865066107@qq.com;wuks@mail.buct.edu.cn
  • Supported by:
    the Excellent Course Project of Beijing University of Chemical Technology(00810220)

Abstract:

After considering the time delay of cell division, the Rotenberg transport equation with time-delay is introduced in this paper. In $L_1$ space, under the condition of non-smooth boundary (the boundary operator is unbounded), it is proved that the transport operator can generate a $C_0$-semigroup. Furthermore, we study the spectrum of the transport operator and prove that the region $\Gamma=\sigma(A_H)\cap \{\lambda\in C | {\rm Re}\lambda>\gamma\}$ ($\gamma>{\rm max}\{\lambda_0, -\sigma_0\}$) is only consists of a finite number of discrete eigenvalues with finite algebraic multiplicity.

Key words: Rotenberg equation, Transport operators, Nonsmooth boundary conditions, Spectrum analysis, Time delay

CLC Number: 

  • O177.2
Trendmd