A NUMERICAL ANALYSIS OF A REACTION-DIFFUSION SYSTEM MODELING THE DYNAMICS OF GROWTH TUMORS

被引：7

作者：

Anaya, Veronica ^{[1
]}

Bendahmane, Mostafa ^{[2
]}

Sepulveda, Mauricio ^{[1
]}

机构：

[1] Univ Concepcion, Dept Ingn Matemat, CI2MA, Concepcion, Chile

[2] Univ Picardie Jules Verne, LAMFA, Fac Math & Informat, Amiens, France

来源：

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2010年 / 20卷 / 05期

关键词：

Reaction-diffusion system; weak solution; existence; finite volume scheme; pattern formation; FINITE-VOLUME SCHEME; FREE-BOUNDARY PROBLEM; MATHEMATICAL-MODEL; TUBULAR STRUCTURES; BIDOMAIN MODEL; CARDIAC TISSUE; STEADY-STATE; CONVERGENCE; CELLS; PROGRESSION;

D O I：

10.1142/S0218202510004428

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a reaction-diffusion system of 2 x 2 equations modeling the spread of early tumor cells. The existence of weak solutions is ensured by a classical argument of Faedo-Galerkin method. Then, we present a numerical scheme for this model based on a finite volume method. We establish the existence of discrete solutions to this scheme, and we show that it converges to a weak solution. Finally, some numerical simulations are reported with pattern formation examples.

引用

页码：731 / 756

页数：26

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