Optimal harvesting of diffusive models in a nonhomogeneous environment

✍ Scribed by Elena Braverman; Leonid Braverman

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 307 KB
• Volume: 71
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2009.04.025

✦ Synopsis

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 ∆(u/K ), where K is the carrying capacity of the environment, rather than ∆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.