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

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....

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Published in:Nonlinear analysis: real world applications 2015-12, Vol.26, p.93-108
Main Authors: Colli, Pierluigi, Gilardi, Gianni, Rocca, Elisabetta, Sprekels, Jürgen
Format: Article
Language:English
Subjects:
Approximation
Asymptotic analysis
Asymptotic properties
Cahn–Hilliard System
Error estimates
Errors
Estimates
Mathematical models
Nonlinearity
Reaction–diffusion equation
Tumor growth
Tumors
Viscosity
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cited_by cdi_FETCH-LOGICAL-c451t-cbb01c296ad9a2c6f4c0f2c0a9a18b7a2d555d8790b9822b3a36004924a743af3
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container_title Nonlinear analysis: real world applications
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creator Colli, Pierluigi
Gilardi, Gianni
Rocca, Elisabetta
Sprekels, Jürgen
description 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.
doi_str_mv 10.1016/j.nonrwa.2015.05.002
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1878-5719
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subjects Approximation
Asymptotic analysis
Asymptotic properties
Cahn–Hilliard System
Error estimates
Errors
Estimates
Mathematical models
Nonlinearity
Reaction–diffusion equation
Tumor growth
Tumors
Viscosity
title Vanishing viscosities and error estimate for a Cahn–Hilliard type phase field system related to tumor growth
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