与年龄相关的半线性时变种群系统的最优捕获

本文讨论了如下的一类与年龄相关的半线性时变种群系统 : p t+ p r+μ( r,t) p +Φ( N ( t) ) p =-v( r,t) p,p( 0 ,t) =∫A0 m( r,t) p( r,t) dr,p( r,0 ) =p0 ( r) ,N ( t) =∫A0 p( r,t) dr,其中 p( r,t)为时刻 t年龄为 r的单种群年龄密度函数 ,v( r,t)为捕获策略 .主要利用泛函分析中的 Mazur定理和分离的思想 ,证明了状态方程解的存在唯一性 ,并论证了对于给定的目标泛函 ,在一定条件下最优捕获控制的存在性 .

Optimal Harvesting for A Semilinear Age-dependent Time-varying Population Systems

A semilinear age dependent time varying population system considered ispt+pr+μ(r,t)p+Φ(N(t))p=-v(r,t)p, p(0,t)=∫ A 0m(r,t)p(r,t) d r, p(r,0)=p 0(r), N(t)=∫ A 0p(r,t) d r,Here p(r,t) denotes the age density distribution at time t and age r, v(r,t) is the control of harvesting. By applying Mazur theory of functional analysis and the ideal of separation, we get the existence and uniqueness for the solution and the existence of the optimal control for given cost function under some assumptions.