  In this paper, we study optimal control problems associated with a scalar
hyperbolic conservation law modeling the development of ovarian follicles.
Changes in the age and maturity of follicular cells are described by a 2D
conservation law, where the control terms act on the velocities. The control
problem consists in optimizing the follicular cell resources so that the
follicular maturity reaches a maximal value in fixed time. Formulating the
optimal control problem within a hybrid framework, we prove necessary
optimality conditions in the form of Hybrid Maximum Principle. Then we derive
the optimal strategy and show that there exists at least one optimal bang-bang
control with one single switching time.
