  We study a moving boundary problem describing the growth of nonnecrotic
tumors in different regimes of vascularisation. This model consists of two
decoupled Dirichlet problem, one for the rate at which nutrient is added to the
tumor domain and one for the pressure inside the tumor. These variables are
coupled by a relation which describes the dynamic of the boundary. By
re-expressing the problem as an abstract evolution equation, we prove local
well-posedness in the small Hoelder spaces context. Further on, we use the
principle of linearised stability to characterise the stability properties of
the unique radially symmetric equilibrium of the problem.
