Sivashinsky equation in a rectangular domain

Bruno Denet (1)

1 IRPHE - Institut de Recherche sur les Phénomènes Hors Equilibre

The (Michelson) Sivashinsky equation of premixed flames is studied in a rectangular domain in two dimensions. A huge number of 2D stationary solutions are trivially obtained by addition of two 1D solutions. With Neumann boundary conditions, it is shown numerically that adding two stable 1D solutions leads to a 2D stable solution. This type of solution is shown to play an important role in the dynamics of the equation with additive noise.

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

Bruno Denet. Sivashinsky equation in a rectangular domain. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2007, 75, pp.046310. ⟨10.1103/PhysRevE.75.046310⟩. ⟨hal-00130593v2⟩