Vanishing viscosities and error estimate for a Cahn–Hilliard type phase field system related to tumor growth. (December 2015)

• Record Type: Journal Article
• Authors: Colli, Pierluigi; Gilardi, Gianni; Rocca, Elisabetta; Sprekels, Jürgen
• Is Part Of: Nonlinear analysis. Volume 26(2015)
• Page Start: 93
• Page End: 108
• Publication Date: 2015-12
• Subjects: Tumor growth -- Cahn–Hilliard System -- Reaction–diffusion equation -- Asymptotic analysis -- Error estimates; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2015.05.002
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: 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 et al. (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.