非光滑边界条件下具时滞的Rotenberg方程主算子的谱分析

数学物理学报 ›› 2022, Vol. 42 ›› Issue (5): 1320-1331.

非光滑边界条件下具时滞的Rotenberg方程主算子的谱分析

童雅阁(),吴开谡*()

^{北京化工大学数理学院北京 100029}

收稿日期:2021-08-12 出版日期:2022-10-26 发布日期:2022-09-30
通讯作者: 吴开谡 E-mail:865066107@qq.com;wuks@mail.buct.edu.cn
作者简介:童雅阁, E-mail: 865066107@qq.com
基金资助:
北京化工大学精品课程项目(00810220)

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

Yage Tong(),Kaisu Wu*()

^{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)

摘要/Abstract

摘要：

该文考虑细胞分裂的时滞性, 引入了具时滞的Rotenberg迁移方程, 在$L_1$空间中非光滑边界条件下(边界算子无界), 证明迁移算子生成$C_0$ -半群, 并进一步分析迁移算子的谱, 得到该迁移算子的谱在区域$\Gamma=\sigma(A_H)\cap \{\lambda\in C | {\rm Re}\lambda>\gamma\}$ ($\gamma>{\rm max}\{\lambda_0, -\sigma_0\}$)中仅由有限个具有有限代数重数的离散本征值组成等结果($\lambda_0, -\sigma_0$的具体意义见正文).

关键词: Rotenberg方程, 迁移算子, 非光滑边界条件, 谱分析, 时滞性

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

中图分类号:

O177.2

童雅阁,吴开谡. 非光滑边界条件下具时滞的Rotenberg方程主算子的谱分析[J]. 数学物理学报, 2022, 42(5): 1320-1331.

Yage Tong,Kaisu Wu. Spectral Analysis of the Main Operator of Rotenberg Equation with Time Delay Under Nonsmooth Boundary Conditions[J]. Acta mathematica scientia,Series A, 2022, 42(5): 1320-1331.

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