Asymptotic analyses and error estimates for a Cahn-Hilliard type phase field system modelling tumor growth

This paper is concerned with a phase field system of Cahn-Hilliard type that is related to a tumor growth model and consists of three equations in terms of the variables order parameter, chemical potential and nutrient concentration. This system has been investigated in some recent contributions from the viewpoint of well-posedness, long time behavior and asymptotic convergence as two positive viscosity coefficients tend to zero at the same time. Here, the authors continue the analysis by showing two independent sets of results as just one of the coefficients tends to zero, the other remaining fixed. Convergence results, uniqueness of solutions to the two resulting limit problems, and suitable error estimates are proved.