We consider a model introduced in [S. Luckhaus, L. Triolo, The continuum reaction–diffusion limit of a stochastic cellular growth model, Rend. Acc. Lincei (S.9) 15 (2004) 215–223] with two species (η and ξ) of particles, representing respectively malignant and normal cells. The basic motions of the η particles are independent random walks, scaled diffusively. The ξ particles move on a slower time scale and obey an exclusion rule among themselves and with the η particles. The competition between the two species is ruled by a coupled birth and death process. We prove convergence in the hydrodynamic limit to a system of two reaction–diffusion equations with measure valued initial data.

Two scale hydrodynamic limit for a model of malignant tumor cells

DE MASI, Anna;
2007-01-01

Abstract

We consider a model introduced in [S. Luckhaus, L. Triolo, The continuum reaction–diffusion limit of a stochastic cellular growth model, Rend. Acc. Lincei (S.9) 15 (2004) 215–223] with two species (η and ξ) of particles, representing respectively malignant and normal cells. The basic motions of the η particles are independent random walks, scaled diffusively. The ξ particles move on a slower time scale and obey an exclusion rule among themselves and with the η particles. The competition between the two species is ruled by a coupled birth and death process. We prove convergence in the hydrodynamic limit to a system of two reaction–diffusion equations with measure valued initial data.
2007
Nous considérons un modèle introduit dans [S. Luckhaus, L. Triolo, The continuum reaction–diffusion limit of a stochastic cellular growth model, Rend. Acc. Lincei (S.9) 15 (2004) 215–223] avec deux espèces de particules (η et ξ) représentant respectivement les cellules malignes et saines. Les mouvements de base des cellules η sont des marches aléatoires indépendantes, sur une échelle diffusive. Les particules ξ se déplacent sur une échelle plus lente et obéissent à une règle d'exclusion entre elles et avec les particules η. La compétition entre les deux espèces est définie par un processus couplé de naissances et morts. Nous prouvons la convergence au sens de la limite hydrodynamique vers un système de deux équations de réaction–diffusion avec données initiales à valeurs mesures.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/18822
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