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.