摘要
讨论了具有迁移现象且环境非均匀的单种群Logistic模型的非负解．利用上、下解方法讨论了非负解的存在性及其渐近状态．
This paper is concerned with the time-dependent classical non-negative solutions for some logistic models of single population in which the species in an ecological model are diffusive and the environment is non-uniform. With a change of the diffuxive behavior, or with a change of the diffusion coefficients, the existence and uniqueness of the species as well as the limiting case when time t→∞are investigated. According to the principle of strong extremum, the eigenvalue theory for the elliptic equation and the properties of the solutions for the parabolic equation, the existence and uniqueness of the solutions under any non-negative and continuous initial conditions are obtained with the sub- and sup- solutions of the model constructed by non-negative steady-state solutions. A critical value d*>0is given such that if the diffusion coefficient of the model satisfies d≥d*, the species will be wanishing exponentially as t→∞. This means that such a species will be extinct. If 0<d<d*, the species will be in a non-negative steady state, or a time-independent but space-dependent state, and will reath equilibrium.
出处
《华中理工大学学报》
CSCD
北大核心
1997年第7期110-112,共3页
Journal of Huazhong University of Science and Technology
关键词
单种群模型
渐近性质
非负解
LOGISTIC模型
single population models
principle of strong extremum
sub-and sup-solutions
asymptotic behavior
