کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4610227 | 1338550 | 2015 | 46 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Existence of pearled patterns in the planar functionalized Cahn–Hilliard equation Existence of pearled patterns in the planar functionalized Cahn–Hilliard equation](/preview/png/4610227.png)
The functionalized Cahn–Hilliard (FCH) equation supports planar and circular bilayer interfaces as equilibria which may lose their stability through the pearling bifurcation: a periodic, high-frequency, in-plane modulation of the bilayer thickness. In two spatial dimensions we employ spatial dynamics and a center manifold reduction to reduce the FCH equation to an 8th order ODE system. A normal form analysis and a fixed-point-theorem argument show that the reduced system admits a degenerate 1:1 resonant normal form, from which we deduce that the onset of the pearling bifurcation coincides with the creation of a two-parameter family of pearled equilibria which are periodic in the in-plane direction and exponentially localized in the transverse direction.
Journal: Journal of Differential Equations - Volume 259, Issue 7, 5 October 2015, Pages 3298–3343