Stability Analysis for an Interface with a Continuous Internal Structure

A general method for solving a linear stability problem of an interface with a continuous internal structure is described. Such interfaces or fronts are commonly found in various branches of physics, such as combustion and plasma physics. It extends simplified analysis of an infinitely thin discontinuous front by means of numerical integration along the steady-state solution. Two examples are presented to demonstrate the application of the method for 1D pulsating instability in magnetic deflagration and 2D Darrieus–Landau instability in a laser ablation wave.