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| 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项的方程组中加入右测自由边界;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: |
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| BIOLOGICAL INVASION PROBLEM WITH FREE BOUNDARY NONLOCAL DIFFUSION EQUATION |
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HE Yu-rong,ZHANG Ya-rong
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| 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 |
