Formal asymptotic limit of a diffuse-interface tumor-growth model

被引：28

作者：

Hilhorst, Danielle ^{[1
]}

Kampmann, Johannes ^{[2
]}

Thanh Nam Nguyen ^{[1
]}

Van Der Zee, Kristoffer George ^{[3
]}

机构：

[1] Univ Paris 11, Math Lab, CNRS, F-91405 Orsay, France

[2] Univ Regensburg, Fak Math, D-93040 Regensburg, Germany

[3] Univ Nottingham, Sch Math Sci, Nottingham NG7 2RD, England

来源：

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2015年 / 25卷 / 06期

关键词：

Reaction-diffusion system; singular perturbation; interface motion; matched asymptotic expansion; tumor-growth model; phase-field model; gradient flow; stabilized Crank-Nicolson method; convex-splitting scheme; CAHN-HILLIARD EQUATION; PHASE FIELD MODEL; SINGULAR LIMIT; SIMULATION; CONVERGENCE; BOUNDARY;

D O I：

10.1142/S0218202515500268

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a diffuse-interface tumor-growth model which has the form of a phase-field system. We characterize the singular limit of this problem. More precisely, we formally prove that as the coefficient of the reaction term tends to infinity, the solution converges to the solution of a novel free boundary problem. We present numerical simulations which illustrate the convergence of the diffuse-interface model to the identified sharp-interface limit.

引用

页码：1011 / 1043

页数：33

共 40 条

[1] The singular limit of the Allen-Cahn equation and the FitzHugh-Nagumo system [J].

Alfaro, Matthieu ;

Hilhorst, Danielle ;

Matano, Hiroshi .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2008, 245 (02) :505-565

[2] CONVERGENCE OF THE CAHN-HILLIARD EQUATION TO THE HELE-SHAW MODEL [J].

ALIKAKOS, ND ;

BATES, PW ;

CHEN, XF .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1994, 128 (02) :165-205

[3] MICROSCOPIC THEORY FOR ANTIPHASE BOUNDARY MOTION AND ITS APPLICATION TO ANTIPHASE DOMAIN COARSENING [J].

ALLEN, SM ;

CAHN, JW .

ACTA METALLURGICA, 1979, 27 (06) :1085-1095

[4] On the closure of mass balance models for tumor growth [J].

Ambrosi, D ;

Preziosi, L .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2002, 12 (05) :737-754

[5] Diffuse-interface methods in fluid mechanics [J].

Anderson, DM ;

McFadden, GB ;

Wheeler, AA .

ANNUAL REVIEW OF FLUID MECHANICS, 1998, 30 :139-165

[6]

[Anonymous], 2010, Multiscale Modeling of Cancer: An Integrated Experimental and Mathematical Modeling Approach

[7]

[Anonymous], 1976, PRINCIPLES MATH ANAL

[8]

Astanin Sergey, 2008, P223, DOI 10.1007/978-0-8176-4713-1_9

[9]

Byrne H, 2003, MATH MED BIOL, V20, P341

[10] GROWTH OF NONNECROTIC TUMORS IN THE PRESENCE AND ABSENCE OF INHIBITORS [J].

BYRNE, HM ;

CHAPLAIN, MAJ .

MATHEMATICAL BIOSCIENCES, 1995, 130 (02) :151-181

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