English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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.

Instability of periodic states for the Sivashinsky equation