The competition-diffusion limit of a stochastic growth model

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.