Existence of solutions for a continuous multigrain model for polymerization

We prove the existence and uniqueness of solutions, for small times, for a mathematical scheme modeling the Ziegler-Natta process of polymerization. The model consists, essentially, of two diffusion problems at two different space scales, one relative to the microscopical catalyst pellets, the other to the macroscopical aggregate of those pellets. The coupling between the two scales is of nonstandard nature.