Stationary solutions and Neumann boundary conditions in the Sivashinsky equation

Bruno Denet (1)

1 IRPHE - Institut de Recherche sur les Phénomènes Hors Equilibre

New stationary solutions of the (Michelson) Sivashinsky equation of premixed flames are obtained numerically in this paper. Some of these solutions, of the bicoalescent type recently described by Guidi and Marchetti, are stable with Neumann boundary conditions. With these boundary conditions, the time evolution of the Sivashinsky equation in the presence of a moderate white noise is controlled by jumps between stationary solutions.

Mots clés: flame instabilities; nonlinear model equation; exact solutions; noise

Domaines: Mécanique des fluides [physics.class-ph]; Systèmes Solubles et Intégrables [nlin.SI]; Formation de Structures et Solitons [nlin.PS]

Bruno Denet. Stationary solutions and Neumann boundary conditions in the Sivashinsky equation. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2006, 74, pp.036303. ⟨10.1103/PhysRevE.74.036303⟩. ⟨hal-00022960⟩