Stationary solutions to phase field crystal equations |
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| Authors: | Morgan Pierre Arnaud Rougirel |
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| Institution: | Laboratoire de Mathématiques et Applications (UMR 6086), Université de Poitiers & CNRS, Téléport 2—BP 30179, Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil Cedex, France |
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| Abstract: | This paper is devoted to the analytical and numerical study of stationary solutions of the one‐dimensional Phase Field Crystal Equation. This new model recently introduced by K. Elder and M. Grant describes phase transformations at the atomic level on large time scales. By using bifurcation methods, we investigate the quantitative and qualitative properties of these solutions: multiplicity, stability, and periodicity. Quite unusual bifurcation diagrams are obtained by numerical simulations. Copyright © 2010 John Wiley & Sons, Ltd. |
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| Keywords: | phase field crystal bifurcation theory higher order elliptic equations |
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