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

VERÓNICA ANAYA

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

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MOSTAFA BENDAHMANE

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

Department of Mathematics, Al-Imam University, Saudi Arabia

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, and

MAURICIO SEPÚLVEDA

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

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https://doi.org/10.1142/S0218202510004428Cited by:4 (Source: Crossref)

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.

Keywords:

AMSC: 35K57, 35K55, 92B05

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