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This paper is concerned with a phase field system of Cahn-Hilliard type thatis related to a tumor growth model and consists of three equations in terms ofthe 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 viscositycoefficients tend to zero at the same time. Here, we continue the analysisperformed in arXiv:1501.07057 [math.AP] by showing two independent sets ofresults as just one of the coefficients tends to zero, the other remainingfixed. We prove convergence results, uniqueness of solutions to the tworesulting limit problems, and suitable error estimates.

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