  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 the recent contributions arXiv:1401.5943
[math.AP] and arXiv:1501.07057 [math.AP] 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, we continue the analysis
performed in arXiv:1501.07057 [math.AP] by showing two independent sets of
results as just one of the coefficients tends to zero, the other remaining
fixed. We prove convergence results, uniqueness of solutions to the two
resulting limit problems, and suitable error estimates.
