Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Instability of periodic states for the Sivashinsky equation

Author: A. Novick-Cohen
Journal: Quart. Appl. Math. 48 (1990), 217-224
MSC: Primary 35B10; Secondary 35K55, 35Q99, 76E99, 80A22
DOI: https://doi.org/10.1090/qam/1052132
MathSciNet review: MR1052132
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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.

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DOI: https://doi.org/10.1090/qam/1052132
Article copyright: © Copyright 1990 American Mathematical Society

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