Global Stability of a Premixed Reaction Zone (Time-Dependent Liñan’s Problem)

Abstract

Global stability properties of a premixed, three-dimensional reaction zone are considered. In the nonadiabatic case (i.e., when there is a heat exchange between the reaction zone and the burned gases) there is a unique, spatially one-dimensional steady state that is shown to be unstable (respectively, asymptotically stable) if the reaction zone is cooled (respectively, heated) by the burned mixture. In the adiabatic case, there is a unique (up to spatial translations) steady state that is shown to be stable. In addition, the large-time asymptotic behavior of the solution is analyzed to obtain sufficient conditions on the initial data for stabilization. Previous partial numerical results on linear stability of one-dimensional reaction zones are thereby confirmed and extended.