【摘要】 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.更多还原

【Abstract】 The existence and uniqueness of Verhulst’s partial differential equations on the population mathematical models were proved under an assumed condition by Schauder’s fixed-point theorem and Gronwall’s lemma.By structuring an enthalpy function,the author shows the asymptotic behavior of the solution with a differential equation.The conclusion is that the weak solution for Verhulst’s partial differential equations on the population mathematical models converges to the stable solution as t→∞ if some hypotheses are imposed.更多还原