Verhulst型人口模型弱解的存在性、唯一性和渐近性

Existence,Uniqueness and Asymptotic Behavior of Global Solutions for Verhulst's Population Mathematical Models

讨论了在一定的假设条件下,Verhulst型人口模型弱解的存在性、唯一性和渐近性.利用Schauder不动点定理,Gronwall引理得到了Verhulst型人口模型弱解的存在性和唯一性,通过构造一个熵函数,推导出了此函数满足的一个微分方程,求解微分方程得到了解的渐近性.主要结论是在一定的假设条件下,Verhulst型人口模型存在唯一的弱解,且当t→∞时弱解趋于稳定.

The existence and uniqueness of Verhulst＇s partial differential equations on the popula- tion mathematical models were proved under an assumed condition by Schauder＇s fixed-point the- orem and Gronwall＇s lemma. By structuring an enthalpy function, the author shows the asymp- totic behavior of the solution with a differential equation. The conclusion is that the weak solu- tion for Verhulst＇s partial differential equations on the population mathematical models converges to the stable solution as t→∞ if some hypotheses are imposed.