Instability of periodic states for the Sivashinsky equation

Publisher Website
Google Scholar
Abstract
The Sivashinsky equation is an asymptotically derived model equation for evolution of the solid-liquid interface which occurs during directional solidification of dilute binary alloys. During the solidification process interfaces are known experimentally to yield planar, cellular, cusped, or dendritic structures. Cellular structures, interpreted here as periodic one dimensional nontrivial steady states, are shown in this paper to be unstable, if they exist, within the context of the Sivashinsky equation. Symmetric nontrivial steady states are likewise shown to be unstable.