Search results for " nonlinear diffusion"

Cross-diffusion driven instability for a nonlinear reaction-diffusion system

2008

In this work we investigate the possibility of the pattern formation for a system of two coupled reaction-diffusion equations. The nonlinear diffusion terms has been introduced to describe the tendency of two competing species to diffuse faster (than predicted by the usual linear diffusion) toward lower densities areas. The reaction terms are chosen of the Lotka-Volterra type in the competitive interaction case. The system is supplemented with the initial conditions and no-flux boundary conditions. Through a linear stability analysis we find the conditions which allow a homogeneous steady state (stable for the kinetics) to become unstable through a Turing mechanism. In particular, we show h…