  In this paper we study a model describing the growth of necrotic tumors in
different regimes of vascularisation. The tumor consists of a necrotic core of
death cells and a surrounding nonnecrotic shell. The corresponding mathematical
formulation is a moving boundary problem where both boundaries delimiting the
nonnecrotic shell are allowed to evolve in time.We determine all radially
symmetric stationary solutions of the problem and reduce the moving boundary
problem into a nonlinear evolution. Parabolic theory provides us the perfect
context in order to show local well-posed of the problem for small initial
data.
