Evans function stability of non-adiabatic combustion waves

In this paper we investigate the linear stability and properties of the planar travelling non–adiabatic combustion front for the cases of zero and non–zero ambient temperature. The speed of the front is estimated numerically using the shooting and relaxation methods. It is shown that for given parameter values the solution either does not exist or there are two solutions with different values of the front speed, which are referred to as ‘fast’ and ‘slow’. The Evans function approach extended by the compound–matrix method is employed to numerically solve the linear–stability problem for the travelling–wave solution. We demonstrate that the ‘slow’ branch of the solutions is unstable, whereas the ‘fast’ branch can be stable or exhibits Hopf or Bogdanov–Takens instability, depending on the parameter values.