The competition-diffusion limit of a stochastic growth model☆

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Abstract

A competition-diffusion system, where populations of healthy and ill cells compete and move on a neutral matrix, is analyzed. A coupled system of nonlinear parabolic equations is derived through a scaling procedure from the microscopic, Markovian dynamics. The space dependent solutions show a behavior markedly different from the associated ODE system. For a large class of initial conditions, the asymptotic behavior of the system can be described through the analysis of associated travelling waves.

Keywords

Tumor growth model
Hydrodynamic limits
Relative entropy method
Reaction-diffusion equation
Travelling waves

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☆

Partially supported by NATO PST.CLG 976552, CNR, and MURST.

a

The authors thank S. Luckhaus, M. Mourragui, E. Presutti, and A. Stevens for useful discussions. E. Saada was supported by the agreement between Universities of Rouen and Roma Tor Vergata, and T. Gobron thanks the Dipartimento di Matematica, Università di Roma Tor Vergata where part of the work was elaborated.

Copyright © 2003 Published by Elsevier Ltd.