Critical slowing-down of spatially nonhomogeneous patterns in a reaction-diffusion model

We exploit the concept of the nonequilibrium potential in order to analize the approach to stationary homogeneous and nonhomogeneous equilibrium states in a bounded bistable reaction-diffusion model. The analysis proceeds through the study of the Lyapunov functional, in terms of a control parameter the threshold parameter phi(c)-in the neighbourhood of a critical point (where a stable and an unstable pattern coalesce), that clearly shows the phenomenon of critical slowing-down in a spatially extended system.