Optimal Harvesting Population Diffusion System With Nonlinear Scale Structure Of The Individual

This paper is the optimal harvest nonlinear population diffusion system with a P-scale structure of the control problem. Use Gronwall inequality, delay and J.L.Lions law theories discuss the existence and uniqueness of solutions of systems, Proved the existence of optimal harvesting control, control is given the necessary conditions for the optimum results obtained for research and optimal harvest population diffusion system with nonlinear control problems scale structure provides a theoretical basis.This paper discusses the model (P):This system (P) is a first-order hyperbolic equations and Laplace equation coupled equations. u(1,t,x) said state variable time t,1scale of the number of individuals in the population space at point x∈Ω. v(1, t, x) represents the individual scale of the rate of change with time;μ(l,t,x)≥0said that the time scale for the individual natural mortality t,l at point x∈Ω in space;Π(N(t,x))≥0said additional mortality of individuals; β(l,t,x;N{t,x)) represents the average rate of population breeding individuals;α(l,t,x) represents the time scale for the populations of t,l harvest rate at point χ∈Ω in the space of individuals; System state function u(l,t,x) depends on the control function α(l,t,x). Referred to as u(l,t,x)=u(l,t,x;α)=u(α).