OPTIMAL HARVESTING IN DIFFUSIVE POPULATION MODELS WITH SIZE RANDOM GROWTH AND DISTRIBUTED RECRUITMENT
In this article, we consider an optimal harvesting control problem for a spatial diffusion population system, which incorporates individual's random growth of size and distributed style of recruitment. The existence and uniqueness of nonnegative solutions to this practical model is established by means of Banach's fixed point theorem. The continuous dependence of population density on the harvesting effort is analyzed. The optimal harvesting strategies are discussed through normal cone and adjoint techniques. Some conditions are presented to assure that there is only one optimal policy.