Optimal harvesting of diffusive models in a nonhomogeneous environment

We study the optimal harvesting strategy for populations whose dynamics is described by reaction-diffusion equations. The production function can be of logistic, Gilpin-Ayala or Gompertz type. The diffusion structure is discussed; we suggest to consider Delta(u=K), where K is the carrying capacity of the environment, rather than Delta u, and study optimal harvesting for models with this diffusion type. Maximum yield is investigated for both continuous and impulsive models. For continuous harvesting, the optimal policy is obtained; for the impulsive equation some limit cases are considered. The paper also outlines a variety of open problems. (C) 2009 Elsevier Ltd. All rights reserved.