| As the human population continues to grow, there is a
need for better management of our natural resources in order for our
planet to be able to produce enough to sustain us. One important
resource we must consider is marine fish populations. The tool of
optimal control is used to investigate harvesting strategies for
maximizing yield of a fish population in a heterogeneous, finite
domain. We determine whether these solutions include no-take marine
reserves as part of the optimal solution. The fishery stock is
modeled using a nonlinear, parabolic partial differential equation
with logistic growth, movement by diffusion and advection, and with
Robin boundary conditions. The objective for the problem is to find
the harvest rate that maximizes the discounted yield. Optimal
harvesting strategies are found numerically. |