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 stabi lity analysis is described by a partial integro-differential equation with a space-dependent coefficient. Accordingly. it involves complicated eigenfu nctions. We show that the analysis can be performed using a finite-order dy namical system in terms of the dynamics of singularities in the complex pla ne, yielding a detailed understanding of the physics of the eigenfunctions and eigenvalues. [S1063-651X(99)01902-9].