On the flow of non-axisymmetric perturbations of cylinders via surface diffusion

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

LeCrone, Jeremy¹  Simonett, Gieri² 

[1] Kansas State Univ, Dept Math, Manhattan, KS 66506 USA

[2] Vanderbilt Univ, Dept Math, Nashville, TN USA

关键词: Surface diffusion;    Well posedness;    Unbounded surfaces;    Maximal regularity;    Nonlinear stability;    Implicit function theorem;   

DOI  :  10.1016/j.jde.2015.12.008

来源: Elsevier

【 摘 要 】

We study the surface diffusion flow acting on a class of general (non-axisymmetric) perturbations of cylinders C-r in IR3. Using tools from parabolic theory on uniformly regular manifolds, and maximal regularity, we establish existence and uniqueness of solutions to surface diffusion flow starting from (spatially-unbounded) surfaces defined over C-r via scalar height functions which are uniformly bounded away from the central cylindrical axis. Additionally, we show that C-r is normally stable with respect to 2 pi-axially-periodic perturbations if the radius r > 1, and unstable if 0 < r < 1. Stability is also shown to hold in settings with axial Neumann boundary conditions. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free