WIAS Preprint No. 2093, (2015)

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


  • Colli, Pierluigi
  • Gilardi, Gianni
    ORCID: 0000-0002-0651-4307
  • Rocca, Elisabetta
    ORCID: 0000-0002-9930-907X
  • Sprekels, Jürgen
    ORCID: 0009-0000-0618-8604

2010 Mathematics Subject Classification

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


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




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 gianni terms of the variables order parameter, chemical potential and nutrient concentration. This system has been investigated in the recent papers citeCGH and citeCGRS gianni from the viewpoint of well-posedness, long time bhv and asymptotic convergence as two positive viscosity coefficients tend to zero at the same time. Here, we continue the analysis performed in citeCGRS by showing two independent sets of results as just one of the coefficents tends to zero, the other remaining fixed. We prove convergence results, uniqueness of solutions to the two resulting limit problems, and suitable error estimates

Appeared in

  • Discrete Contin. Dyn. Syst., 10 (2017), pp. 37--54.

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