Nonlinear stability in reaction–diffusion systems via optimal Lyapunov functions

We define optimal Lyapunov functions to study nonlinear stability of constant solutions to reaction–diffusion systems. A computable and finite radius of attraction for the initial data is obtained. Applications are given to the well-known Brusselator model and a three-species model for the spatial spread of rabies among foxes. © 2007 Elsevier Inc. All rights reserved