The onset of linear instabilities in a solid combustion model

This article concerns the onset of linear instability in a simple model of solid combustion in a semi-infinite two-dimensional strip of width l. The f ree boundary problem that describes the model involves initial and boundary conditions, including a nonlinear kinetic condition at the interface. The linear problem governing perturbations to a basic solution is solved by the method of images with the reaction front perturbation satisfying an integr odifferential equation, This equation is then solved using Laplace transfor ms. Finally, we perform a stability analysis for the model by studying the solution of the reaction front perturbation. The inclusion of initial condi tions enables us to show the development of linear instability from arbitra ry initial small disturbances.