广西师范大学学报（自然科学版） ›› 2023, Vol. 41 ›› Issue (1): 17-23.doi: 10.16088/j.issn.1001-6600.2022061703

• 综述 • 上一篇    下一篇

三类区域上的Logistic扩散问题及其分析

张梦芸1, 葛静2, 林支桂3*   

  1. 1.南京财经大学应用数学学院, 江苏 南京 210003;
    2.淮阴师范学院数学与统计学院, 江苏 淮安 223300;
    3.扬州大学数学科学学院, 江苏 扬州 225002
  • 收稿日期:2022-06-17 修回日期:2022-07-18 出版日期:2023-01-25 发布日期:2023-03-07
  • 通讯作者: 林支桂(1965—),男,江苏兴化人,扬州大学教授,博导。E-mail:zglin@yzu.edu.cn
  • 基金资助:
    国家自然科学基金 (12271470, 11701206, 12101301, 11911540464)

Logistic Diffusion Problem and Its Analysis on Three Types of Domains

ZHANG Mengyun1, GE Jing2, LIN Zhigui3*   

  1. 1. School of Applied Mathematics, Nanjing University of Finance Economics, Nanjing Jiangsu 210003, China;
    2. School of Mathematics and Statistics, Huaiyin Normal University, Huaian Jiangsu 223300, China;
    3. School of Mathematical Science, Yangzhou University, Yangzhou Jiangsu 225002, China
  • Received:2022-06-17 Revised:2022-07-18 Online:2023-01-25 Published:2023-03-07

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摘要： 本文介绍几类不同区域上的反应扩散问题, 这些问题描述了种群的空间扩张现象。对比经典的Cauchy问题,本文给出固定区域、演化区域和自由边界上的扩散问题, 根据相应问题的理论结果, 分析不同区域上扩散的区别和联系。

关键词: 反应扩散, 自由边界, 演化区域, 扩张和灭绝

Abstract: Reaction-diffusion problems in several different types of domains are investigated in this paper, which describes spatial expansion of population. Compared with the classical Cauchy problem, diffusion problems are presented in fixed domains, evolving domains and free boundaries. According to the theoretical results of the corresponding problems, the differences and connections of diffusion in different domains are analyzed.

Key words: reaction-diffusion, free boundary, evolving domain, expansion and extinction

中图分类号: 

  • O29
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