  We study a diffuse interface model describing the evolution of the flow of a
binary fluid in a Hele-Shaw cell. The model consists of a Cahn-Hilliard-Darcy
(CHD) type system with transport and mass source. A relevant physical
application is related to tumor growth dynamics, which in particular justifies
the occurrence of a mass inflow. We study the initial-boundary value problem
for this model and prove global existence and uniqueness of strong solutions in
two space dimensions as well as local existence in three space dimensions.
