Optimal harvesting for a size-stage-structured population model

In this paper, we consider the optimal harvesting for a size-stage-structured population model. The main feature of this article is to study optimal harvesting, stage structure and body size at the same time in a single population system. At first, under appropriate assumptions, by the method of characteristic and simple changes of variables, we obtain the properties of solutions of our model, including the global existence and uniqueness, nonnegativity and boundedness. Then, we give several useful estimates about the solutions. Taking advantage of these estimates and relevant theory of functional analysis, we derive the existence of optimal harvesting strategy. Finally, a discussion of related problems is also presented.