Flame front propagation V: Stability Analysis of Flame Fronts: Dynamical Systems Approach in the Complex Plane

Details Flame front propagation V: Stability Analysis of Flame Fronts: Dynamical Systems Approach in the Complex Plane Flame front propagation V: Stability Analysis of Flame Fronts: Dynamical Systems Approach in the Complex Plane

2003-02-11

arxiv.org/abs/nlin/0302020v2

Phys. Rev. E 59, 2587-2593 (1999)

Nonlinear Sciences

Pattern Formation and Solitons

17 pages 7 figures

Scientific paper

10.1103/PhysRevE.59.2587

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.

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