Stability analysis of flame fronts: Dynamical systems approach in the complex plane

We consider flame front propagation in channel geometries. The steady-state solution in this problem is space dependent and therefore the linear stability analysis is described by a partial integro-differential equation with a space-dependent coefficient. Accordingly, it involves complicated eigenfunctions. We show that the analysis can be performed using a finite-order dynamical system in terms of the dynamics of singularities in the complex plane, yielding a detailed understanding of the physics of the eigenfunctions and eigenvalues.