Stationary Solutions to Phase Field Crystal Equations

Morgan Pierre (1) , Arnaud Rougirel (1)

1 LMA [Poitiers] - Laboratoire de mathématiques et applications [UMR 6086]

This paper is devoted to the analytical and numerical study of the 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 atomistic level on large time scales. By using bifurcation methods, we investigate quantitative and qualitative properties of these solutions: multiplicity, stability, periodicity. Quite unusual bifurcation diagrams are obtained by numerical simulations.

Mots clés: Phase Field Crystal; Bifurcation Theory; Higher Order Elliptic Equations

Domaines: Equations aux dérivées partielles [math.AP]

Morgan Pierre, Arnaud Rougirel. Stationary Solutions to Phase Field Crystal Equations. 2009. ⟨hal-00407353⟩