增长区域上具有弱Allee效应的扩散模型  

Diffusive model with weak Allee effect on a growing domain

作　　者：朱家桢[1] 林支桂[1] ZHU Jiazhen;LIN Zhigui(School of Mathematical Science,Yangzhou University,Yangzhou 225002,China)

机构地区：[1]扬州大学数学科学学院,江苏扬州225002

出　　处：《扬州大学学报（自然科学版）》2020年第5期15-18,共4页Journal of Yangzhou University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11771381,11911540464).

摘　　要：为理解栖息区域的增长对物种生存的影响,提出增长区域上一类具有弱Allee效应的反应扩散模型.当物种生存区域的增长是各向同性时,通过将模型转换成固定区域上的反应扩散问题,给出了稳态解的存在唯一性;由上下解方法得到模型解的渐近性态,并通过对比固定区域与增长区域上物种的可持续生存性,给出相应的生物学解释.结果表明,区域的有限增长对物种的生存有积极的作用.In order to understand the impact of the growth of habitat on the survival of species,this paper studies a reaction-diffusion model with weak Allee effect on a growing domain.Assuming that the growth of habitat is isotropic,the model is converted into a reaction-diffusion problem on a fixed domain,and then the existence and uniqueness of the steady state solution are given.By using the upper and lower solution method,the asymptotic behavior of the solution to the reaction-diffusion problem is reveled.The corresponding biological explanation is given under the comparison of the sustainable survivability of the species on a fixed domain with that on a growing domain.It is concluded that the finite growth of habitat benefits the survival of species with weak Allee growth.

关 键 词：反应扩散问题 弱Allee效应 增长区域 全局渐近性 

分 类 号：O175.26[理学—数学]