  We consider the problem of the long time dynamics for a diffuse interface
model for tumor growth. The model describes the growth of a tumor surrounded by
host tissues in the presence of a nutrient and consists in a Cahn-Hilliard-type
equation for the tumor phase coupled with a reaction-diffusion equation for the
nutrient concentration. We prove that, under physically motivated assumptions
on parameters and data, the corresponding initial-boundary value problem
generates a dissipative dynamical system that admits the global attractor in a
proper phase space.
