Pulsating instabilities in the Zeldovich-Liñán model

In this paper we numerically study the properties and stability of the travelling combustion waves in Zeldovich-Liñán model in the adiabatic limit in one-dimension. The structure and the properties of the combustion waves are found to be different for the fast and slow recombination regimes. The dependence of flame speed on the parameters of the model are studied in detail. The results are compared to the prediction of the activation energy asymptotic analysis. Stability of combustion waves is studied by using the Evans function method and direct integration of the governing partial differential equations. It is demonstrated that the combustion waves lose stability due to the supercritical Hopf bifurcation. The neutral stability boundary is found in the space of parameters. The pulsating solutions emerging as a result of Hopf bifurcation are also investigated. AMS classification scheme numbers: 35K57, 80A25