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 free 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 integro‐differential equation. This equation is then solved using Laplace transforms. Finally, we perform a stability analysis for the model by studying the solution of the reaction front perturbation. The inclusion of initial conditions enables us to show the development of linear instability from arbitrary initial small disturbances.