# A Population Harvesting Model with Time and size Competition Dependence Function

In this work, we are interested in the problem of forest management. We consider a nonlinear model describing the forest harvesting of a size-structured tree population with intra-specific competition, where the population competes with trees of larger size. Our objectives are to maximize the revenues from timber production while maintaining the regeneration of the forest and meeting the demand for wood from the current and future populations. A fixed-point argument is used to prove the existence and uniqueness of a solution to the nonlinear problem. Then, the optimal control problem is studied, where the existence of an optimal control is proved and its characterization is given by an optimality necessary condition.

References

[1] A. Calsina, J. Saldana, A model of physiologically structured population dynamics with a nonlinear individual growth rate. J. Math. Biol.,33, 335-364 (1995).

[2] N. Kato, Optimal harvesting for nonlinear size-structured population dynamics. J. Math. Anal. Appl., 342(2), 1388-1398 (2008).