  We study an initial-boundary value problem (IBVP) for a coupled
Cahn-Hilliard-Hele-Shaw system that models tumor growth. For large initial data
with finite energy, we prove global (local resp.) existence, uniqueness, higher
order spatial regularity and Gevrey spatial regularity of strong solutions to
the IBVP in 2D (3D resp.). Asymptotically in time, we show that the solution
converges to a constant state exponentially fast as time tends to infinity
under certain assumptions.

Analysis of PDEs;Pattern Formation and Solitons;Biological Physics;Quantitative Methods