|
| 摘要: |
| 为了更好地描述生物入侵现象，本文引入了具有自由边界的生物入侵模型。首
先，在具有 Logistic 项的方程中加入右自由边界；其次，利用 Sobolev 嵌入定理和比较原
理证明了方程局部解的存在唯一性;最后，根据红火蚁的相关研究数据和内容，假设在不受
外界干扰的情况下，模拟红火蚁的扩散面积和巢数。本文主要模拟了红火蚁的早期扩散过
程。在扩散初期，红火蚁的传播比较缓慢，达到一定数量后才大面积扩散。 |
| 关键词: 自由边界 生物入侵 微分方程 |
| DOI： |
| 分类号:O175.27 |
| 基金项目:国家自然科学基金青年项目 (12101482)，中国博士后科学基金 (2022M722604), 陕西省重点研发-社会发展领域一般项目 (No.2023-JC-QN-0016)，陕西数理科学基础研究项目(23JSQ042) |
|
| Biological invasion problem with free boundary nonlocal diffusion equation |
|
Yurong He,Yarong Zhang
|
| Abstract: |
| In order to better describe the phenomenon of biological invasion, this paper
introduces a free boundary model of biological invasion. Firstly, the right free boundary is added
to the equation with logistic terms. Secondly, the existence and uniqueness of local solutions are
proved by the Sobolev embedding theorem and the comparison principle. Finally, according to the
relevant research data and contents of red fire ants, the diffusion area and nest number of red fire
ants were simulated without external disturbance. This paper mainly simulates the early diffusion
process of red fire ants. In the early diffusion stage, red fire ants grow slowly and then spread over
a large area after reaching a certain number. |
| Key words: Free boundary biological invasion differential equation |
