Verhulst型偏微分方程人口模型整体解的存在唯一性研究(Ⅰ)

The Existence and Uniqueness of Global Solutions for Verhulst's Partial Differential Equations on the Population Mathematical Models

本文讨论了Ｖｅｒｈｕｌｓｔ型偏微分方程人口模型ｐｔ（ｔ，ｘ） ＋ ｐｘ （ｔ，ｘ） ＝ － ｄ１（ｘ） ＋ Ｋ∫Ａ０ ｐ（ｔ，ξ）ｄξｐ（ｔ，ｘ） （１）在一定非局部初边值条件下的解，运用逐次逼近法得到了方程（１）迭代解的表达式，并证明了它的整体存在唯一性。

The solutions of Verhulst’s partial differential equations an the human population mathematical model,Pt(t,x)+Px(t,x)=-d 1(x)+K∫ A 0P(t,ξ)dξp(t,x)under the particular non-local initial and border conditions, are discussed. The formula of iterative solutions for this equation are obtained by the successive approximation method. The theorem on the global existence and uniqueness of solutions for this equation are also theoritically proved.