A competition-diffusion system, where populations of healthy and malignant cells compete and move on a neutral matrix, is analyzed. A coupled system of degenerate nonlinear parabolic equations is derived through a scaling procedure from the microscopic, Markovian dynamics. The healthy cells move much slower than the malignant ones, such that no diffusion for their density survives in the limit. The malignant cells may locally accumulate, while for the healthy ones an exclusion rule is considered. The asymptotic behavior of the system can be partially described through the analysis of the stationary wave which connects different equilibria.
@article{RLIN_2004_9_15_3-4_215_0,
author = {Stephan Luckhaus and Livio Triolo},
title = {The continuum reaction-diffusion limit of a stochastic cellular growth model},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
volume = {15},
year = {2004},
pages = {215-223},
zbl = {1162.60346},
mrnumber = {2148880},
language = {en},
url = {http://dml.mathdoc.fr/item/RLIN_2004_9_15_3-4_215_0}
}
Luckhaus, Stephan; Triolo, Livio. The continuum reaction-diffusion limit of a stochastic cellular growth model. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 15 (2004) pp. 215-223. http://gdmltest.u-ga.fr/item/RLIN_2004_9_15_3-4_215_0/
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