Porous Medium Combustion

I shall study a model of porous medium combustion, derived by Norbury and Stuart [1], restricting attention to the class of travelling wave solutions. Under this simplifying assumption the model reduces to a fifth—order system of coupled, nonlinear ordinary differential equations with a discontinuous forcing term (this corresponds to the reaction rate and is discontinuous because of the high energy activation asymptotics involved) and three free parameters (λ,μ,a). The form of the reaction rate enables us to deduce the existence of only four types of solution to the model, each solution characterised by the manner in which the reaction is activated and terminated.The aim of my talk will, then, be to describe how the path-following package AUTO can be used to determine the degeneracy—, or bifurcation—, surfaces which separate the different classes of solutions in the three-dimensional parameter space. In this way it should then be possible to predict what type of solution will occur for given values of the parameters (λ,μ,a).