Flame front propagation V: 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 to required detail using a finite order dynamical system in terms of the dynamics of singularities in the complex plane, yielding detailed understanding of the physics of the eigenfunctions and eigenvalues.