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

被引：48

作者：

Colli, Pierluigi ^{[1
]}

Gilardi, Gianni ^{[1
]}

Rocca, Elisabetta ^{[2
,3
]}

Sprekels, Juergen ^{[2
,4
]}

机构：

[1] Univ Pavia, Dipartimento Matemat F Casorati, I-27100 Pavia, Italy

[2] Weierstrass Inst Appl Anal & Stochast, D-10117 Berlin, Germany

[3] Univ Milan, Dipartimento Matemat F Enriques, I-20133 Milan, Italy

[4] Humboldt Univ, Dept Math, D-10099 Berlin, Germany

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2015年 / 26卷

关键词：

Tumor growth; Cahn-Hilliard System; Reaction-diffusion equation; Asymptotic analysis; Error estimates; MODELS; INVASION;

D O I：

10.1016/j.nonrwa.2015.05.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：93 / 108

页数：16

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