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 (eta and xi) of particles, representing respectively malignant and normal cells. The basic motions of the eta particles are independent random walks, scaled diffusively. The xi particles move on a slower time scale and obey an exclusion rule among themselves and with the eta 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. (c) 2006 Elsevier Masson SAS. All rights reserved.
De Masi, A., Luckhaus, S., Presutti, E. (2007). Two scales hydrodynamic limit for a model of malignant tumor cells. ANNALES DE L'INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 43(3), 257-297 [10.1016/j.anihpb.2006.03.003].
Two scales hydrodynamic limit for a model of malignant tumor cells
PRESUTTI, ERRICO
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 (eta and xi) of particles, representing respectively malignant and normal cells. The basic motions of the eta particles are independent random walks, scaled diffusively. The xi particles move on a slower time scale and obey an exclusion rule among themselves and with the eta 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. (c) 2006 Elsevier Masson SAS. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
