空间分布非均匀的Logistic模型及其最优收获

Logistic Model with Spatial Nonhomogeneous Diffusion and its Optimal Harvest Policy

本文考虑空间分布非均匀且生产函数为关于E ,u变量可分离的形式为一般的H(E(x) )G(u)型函数的Logistic模型 u t =DΔu+r(x)u1 - uK(x) -H(E(x) )G(u) ,(t,x) ∈ ( 0 ,∞ ) ×Ω ,u( 0 ,x) =φ(x) ,x∈Ω , u n =0 ,(t,x) ∈ ( 0 ,∞ ) ,x∈ Ω .在一些合理的假设条件下 ,得到了与用常微分方程表示的空间分布均匀的Logistic模型[1 3 ] 相平行的结论 ,所得到的结果也推广了文献 [4]的相关结果 .

A spatial nonhomogeneous Logistic modelut=DΔu+r(x)u1-uK(x)-H(E(x))G(u),(t,x)∈(0,∞)×Ω, u(0,x)=φ(x),x∈Ω, un=0,(t,x)∈(0,∞),x∈Ω,with productive function H(E(x))G(u) is considered in this paper.Under some reasonable assumptation,we derive parelleling results to that of Logistic model with spatial homogeneous represented by ordinary differential equations [1-3].Our brief results also generalize the corresponding results in [4].