A NUMERICAL ANALYSIS OF A REACTION–DIFFUSION SYSTEM MODELING THE DYNAMICS OF GROWTH TUMORS-Reference-Cited by-同舟云学术

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

Published:2010-05 Issue:05 Volume:20 Page:731-756
ISSN:0218-2025
Container-title:Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:Math. Models Methods Appl. Sci.

Author:

ANAYA VERÓNICA¹,BENDAHMANE MOSTAFA²³,SEPÚLVEDA MAURICIO⁴

Affiliation:

1. Departamento de Ingenieria Matematica, Universidad de Concepcion, Casilla 160-C, Concepcion, Chile

2. Faculté de Mathématiques et d'Informatique, LAMFA, Université de Picardie Jules Verne, Amiens, France

3. Department of Mathematics, Al-Imam University, Saudi Arabia

4. CI2MA, Departamento de Ingenieria Matematica, Universidad de Concepcion, Casilla 160-C, Concepcion, Chile

Abstract

We consider a reaction–diffusion system of 2 × 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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218202510004428

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