Harvesting renewable resources of population with size structure and diffusion. (English) Zbl 1406.92702

Xie, Qiang-Jun; He, Ze-Rong; Zhang, Chun-Guo

Abstr. Appl. Anal. 2014, Article ID 396420, 9 p. (2014).

Summary: The aim of this work is to explore the optimal exploitation way for a biological resources model incorporating individual’s size difference and spatial effects. The existence of a unique nonnegative solution to the state system is shown by means of Banach’s fixed point theorem, and the continuous dependence of the population density with the harvesting effort is given. The optimal harvesting strategy is established via normal cone and adjoint system technique. Some conditions are found to assure that there is only one optimal policy.

MSC:

92D40	Ecology
92D25	Population dynamics (general)
91B76	Environmental economics (natural resource models, harvesting, pollution, etc.)
49N90	Applications of optimal control and differential games
35Q92	PDEs in connection with biology, chemistry and other natural sciences

Keywords:

harvesting renewable resources; optimal exploitation; population density

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