WIAS Preprint No. 2077, (2015)

Vanishing viscosities and error estimate for a Cahn--Hilliard type phase field system related to tumor growth


  • Colli, Pierluigi
    ORCID: 0000-0002-7921-5041
  • Gilardi, Gianni
    ORCID: 0000-0002-0651-4307
  • Rocca, Elisabetta
    ORCID: 0000-0002-9930-907X
  • Sprekels, Jürgen

2010 Mathematics Subject Classification

  • 35Q92 92C17 35K35 35K57 78M35 35B20 65N15 35R35


  • Tumor growth, Cahn--Hilliard system, reaction-diffusion equation, asymptotic analysis, error estimates




In this paper we perform an asymptotic analysis for two different vanishing viscosity coefficients occurring in a phase field system of Cahn--Hilliard type that was recently introduced in order to approximate a tumor growth model. In particular, we extend some recent results obtained in [Colli-Gilardi-Hilhorst 2015], letting the two positive viscosity parameters tend to zero independently from each other and weakening the conditions on the initial data in such a way as to maintain the nonlinearities of the PDE system as general as possible. Finally, under proper growth conditions on the interaction potential, we prove an error estimate leading also to the uniqueness result for the limit system.

Appeared in

  • Nonlinear Anal. Real World Appl., 26 (2015) pp. 93--108.

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