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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2023, Vol. 40 ›› Issue (3): 503-510.doi: 10.3969/j.issn.1005-3085.2023.03.013

• • 上一篇    

具有信号相关灵敏度和Logistic源的完全抛物型吸引–排斥趋化系统解的渐近行为

周新露,  李中平   

  1. 西华师范大学数学与信息学院，南充 637009
  • 收稿日期:2020-12-14 接受日期:2021-03-29 出版日期:2023-06-15 发布日期:2023-08-15
  • 通讯作者: 李中平 E-mail: zhongpingli80@126.com
  • 基金资助:
    国家自然科学基金 (11301419)；西华师范大学科研创新团队 (CXTD2020-5).

Asymptotic Behavior of Solution to a Fully Parabolic Attraction-repulsion Chemotaxis System with Signal-dependent Sensitivities and Logistic Source

ZHOU Xinlu,  LI Zhongping   

  1. School of Mathematics and Information, China West Normal University, Nanchong 637009
  • Received:2020-12-14 Accepted:2021-03-29 Online:2023-06-15 Published:2023-08-15
  • Contact: Z. Li. E-mail address: zhongpingli80@126.com
  • Supported by:
    The National Natural Science Foundation of China (11301419); the Research and Innovation Team of China West Normal University (CXTD2020-5).

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摘要：

生物趋化性是细胞在化学物质的作用下沿物质浓度梯度方向所做的定向运动，依据对刺激源的靠近或远离又可以分为正趋化性和负趋化性，这种特性对生物体的生存和发展具有重要的意义。对趋化现象的研究在生物采油、生态除污、生物群体动力学、传染病发病原理等领域都有着十分重要的意义。为此，在齐次Neumann边界条件下对一类具有信号相关灵敏度和Logistic源的完全抛物型吸引–排斥趋化系统进行了研究。通过构造能量泛函，在初值及趋化灵敏度函数满足一定的条件下，得到了系统全局有界解的渐近行为。结果表明，系统的解最终会呈指数收敛到一个稳定的状态。

关键词: 渐近行为, 完全抛物, 吸引–排斥, 趋化, Logistic源

Abstract:

Chemotaxis is a phenomenon of the directed movement of cells in response to the concentration gradient of the chemical signal substance which is produced by cells. It can be divided into positive chemotaxis and negative chemotaxis according to the proximity or distance to the stimuli, which is meaningful to the survival and development of organisms. The study of chemotaxis is of great significance in the fields of biological oil recovery, ecological decontamination, biological population dynamics and the pathogenesis of infectious diseases. Therefore, a class of fully parabolic attraction-repulsion chemotaxis system with signal-dependent sensitivities and Logistic source is studied under homogeneous Neumann boundary conditions. The asymptotic behavior of the global bounded solution of the system is investigated by constructing an appropriate energy functional when it meets initial data and sensitivity functions satisfying some conditions. The result shows that the solution of the system will eventually converge to a constant steady state exponentially.

Key words: asymptotic behavior, fully parabolic, attraction-repulsion, chemotaxis, Logistic source

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