title: Sivashinsky equation in a rectangular domain.
abstract: The (Michelson) Sivashinsky equation of premixed flames is studied in a rectangular domain in two dimensions. A huge number of two-dimensional (2D) stationary solutions are trivially obtained by the 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.
authors.affiliation: IRPHE, 49 rue Joliot Curie, BP 146, Technopole de Chateau Gombert, 13384 Marseille, Cedex 13, France. bruno.denet@irphe.univ-mrs.fr
authors.forename: Bruno
authors.initials: B
authors.lastname: Denet