BIOLOGICAL INVASION PROBLEM WITH FREE BOUNDARY NONLOCAL DIFFUSION EQUATION  

具有自由边界的非局部扩散方程的生物入侵问题

作　　者：HE Yu-rong ZHANG Ya-rong 何毓容;张雅荣(西安建筑科技大学理学院,西安710055;西安特种设备检验检测院,西安710055;西北工业大学能动学院,西安710072)

机构地区：[1]School of Science,Xi'an University of Architecture and Technology,Xi'an 710055,China [2]Xi'an Special Equipment Inspection Institute,Xi'an 710065,China [3]School of Power and Energy,Northwestern Polytechnical University,Xi'an 710072,China

出　　处：《数学杂志》2025年第1期48-56,共9页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(12101482);Postdoctoral Science Foundation of China(2022M722604);General Project of Science and Technology of Shaanxi Province(2023-YBSF-372);The Natural Science Foundation of Shaan Xi Province(2023-JCQN-0016);Shannxi Mathmatical Basic Science Research Project(23JSQ042)。

摘　　要：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.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：Free boundary biological invasion differential equation 

分 类 号：O175.27[理学—数学]