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In this paper, we study a vector conservation law that models the growth andselection of ovarian follicles. During each ovarian cycle, only a definitenumber of follicles ovulate, while the others undergo a degeneration processcalled atresia. This work is motivated by a multiscale mathematical modelstarting on the cellular scale, where ovulation or atresia result from ahormonally controlled selection process. A two-dimensional conservation lawdescribes the age and maturity structuration of the follicular cellpopulations. The densities intersect through a coupled hyperbolic systembetween different follicles and cell phases, which results in a vectorconservation law and coupling boundary conditions. The maturity velocityfunctions possess both a local and nonlocal character. We prove the existenceand uniqueness of the weak solution to the Cauchy problem with bounded initialand boundary data.

Cauchy problem for multiscale conservation laws: Application to structured cell populations