The continuum reaction-diffusion limit of a stochastic cellular growth model

Stephan Luckhaus; Livio Triolo

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2004)

  • Volume: 15, Issue: 3-4, page 215-223
  • ISSN: 1120-6330

Abstract

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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.

How to cite

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Luckhaus, Stephan, and 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 15.3-4 (2004): 215-223. <http://eudml.org/doc/252410>.

@article{Luckhaus2004,
abstract = {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.},
author = {Luckhaus, Stephan, Triolo, Livio},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Tumor growth model; Hydrodynamic limits; Degenerate Reaction-Diffusion system},
language = {eng},
month = {12},
number = {3-4},
pages = {215-223},
publisher = {Accademia Nazionale dei Lincei},
title = {The continuum reaction-diffusion limit of a stochastic cellular growth model},
url = {http://eudml.org/doc/252410},
volume = {15},
year = {2004},
}

TY - JOUR
AU - Luckhaus, Stephan
AU - Triolo, Livio
TI - The continuum reaction-diffusion limit of a stochastic cellular growth model
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2004/12//
PB - Accademia Nazionale dei Lincei
VL - 15
IS - 3-4
SP - 215
EP - 223
AB - 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.
LA - eng
KW - Tumor growth model; Hydrodynamic limits; Degenerate Reaction-Diffusion system
UR - http://eudml.org/doc/252410
ER -

References

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  11. KLAASEN, G.A. - TROY, W.C., The stability of traveling wave front solutions of a reaction-diffusion system. SIAM J. Appl. Math., 41, 1981, 145-167. Zbl0467.35011MR622879DOI10.1137/0141011
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  13. MARCHANT, B.P. - NORBURY, J. - PERUMPANANI, A.J., Traveling shock waves arising in a model of malignant invasion. SIAM J. Appl. Math., 60, 2000, 463-476. Zbl0944.34021MR1740255DOI10.1137/S0036139998328034
  14. PERRUT, A., Hydrodynamic limits for a two-species reaction-diffusion process. Annals of Appl. Probab., 10, 2000, 163-191. Zbl1171.60394MR1765207DOI10.1214/aoap/1019737668
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