Dimensional reduction of a bushfire model

Throw a match into a vegetation layer. What happens to the fire as time goes on? The spread from the ground to canopy, and along the terrain may be modelled by a simple two-dimensional reaction-diffusion system. We discuss the use of centre manifold theory to simplify a two-dimensional model of fire spread down to a one-dimensional model of fire propagation along the layer. This not only shows how to justify such simple one-dimensional models, it is also possible, for example, to determine the reaction wave speed analytically.