On a Cahn-Hilliard type phase field system related to tumor growth

Abstract

The paper deals with a phase field system of Cahn-Hilliard type. For positive viscosity coefficients, the authors prove an existence and uniqueness result and study the long time behavior of the solution by assuming the nonlinearities to be rather general. In a more restricted setting, the limit as the viscosity coefficients tend to zero is investigated as well.

Key words: phase field model, tumor growth, viscous Cahn-Hilliard equations, well posedness, long-time behavior, asymptotic analysis