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

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• 作者：Jeremy LeCrone^a ; ^{lecronjs@ksu.edu" class="auth_mail" title="E-mail the corresponding author} ; ; Gieri Simonett^b ; ^{gieri.simonett@vanderbilt.edu" class="auth_mail" title="E-mail the corresponding author} ;
• 关键词：primary ; 35K93 ; 53C44 ; secondary ; 35B35 ; 35B32 ; 46T20
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：15 March 2016
• 年：2016
• 卷：260
• 期：6
• 页码：5510-5531
• 全文大小：381 K

文摘

We study the surface diffusion flow acting on a class of general (non-axisymmetric) perturbations of cylinders C_r${\mathcal{C}}_r$ in IR³$\mathrm{I}{\mathrm{R}}^3$. 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${\mathcal{C}}_r$ via scalar height functions which are uniformly bounded away from the central cylindrical axis. Additionally, we show that C_r${\mathcal{C}}_r$ is normally stable with respect to 2π  -axially-periodic perturbations if the radius r>1$r>1$, and unstable if 0<r<1$0<r<1$. Stability is also shown to hold in settings with axial Neumann boundary conditions.