  In this paper, we study a vector conservation law that models the growth and
selection of ovarian follicles. During each ovarian cycle, only a definite
number of follicles ovulate, while the others undergo a degeneration process
called atresia. This work is motivated by a multiscale mathematical model
starting on the cellular scale, where ovulation or atresia result from a
hormonally controlled selection process. A two-dimensional conservation law
describes the age and maturity structuration of the follicular cell
populations. The densities intersect through a coupled hyperbolic system
between different follicles and cell phases, which results in a vector
conservation law and coupling boundary conditions. The maturity velocity
functions possess both a local and nonlocal character. We prove the existence
and uniqueness of the weak solution to the Cauchy problem with bounded initial
and boundary data.
