具结构化的细菌种群增生中迁移方程解的渐近稳定性分析

数学物理学报 ›› 2022, Vol. 42 ›› Issue (3): 807-817.

具结构化的细菌种群增生中迁移方程解的渐近稳定性分析

吴红星*(),袁邓彬,王胜华

^{上饶师范学院江西上饶 334001}

收稿日期:2019-08-27 出版日期:2022-06-26 发布日期:2022-05-09
通讯作者: 吴红星 E-mail:jxsruwhx@163.com
基金资助:
国家自然科学基金(11861053);国家自然科学基金(11461055);江西省教育厅科技项目(GJJ201714);上饶市科技项目(2020L007)

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

Hongxing Wu*(),Dengbin Yuan,Shenghua Wang

^{Shangrao Normal University, Jiangxi Shangrao 334001}

Received:2019-08-27 Online:2022-06-26 Published:2022-05-09
Contact: Hongxing Wu E-mail:jxsruwhx@163.com
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)

摘要/Abstract

摘要：

该文借助于线性算子理论，探讨了以细菌种群为背景的具结构化的更一般的边界条件的迁移方程, 运用预解算子和比较算子等方法证明了该迁移方程相应迁移算子谱在带域 $\Gamma_{\alpha, \beta}$ 中仅由有限个具有限代数重数的离散本征值构成, 证明了该迁移方程解在 $\psi_0 \in D (A_{H_{\alpha, \beta}})$ 时是渐近稳定的.

关键词: 细菌种群, 迁移方程, 离散本征值, 渐近稳定性

Abstract:

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

中图分类号:

O177.2

吴红星,袁邓彬,王胜华. 具结构化的细菌种群增生中迁移方程解的渐近稳定性分析[J]. 数学物理学报, 2022, 42(3): 807-817.

Hongxing Wu,Dengbin Yuan,Shenghua Wang. Asymptotic Stability Analysis of Solutions to Transport Equations in Structured Bacterial Population Growth[J]. Acta mathematica scientia,Series A, 2022, 42(3): 807-817.

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