We study the surface diffusion flow acting on a class of general (non--axisymmetric) perturbations of cylinders Cr 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 Cr via scalar height functions which are uniformly bounded away from the central cylindrical axis. Additionally, we show that Cr is normally stable with respect to 2π--axially--periodic perturbations if the radius r>1,and unstable if 0
Copyright © 2016 Elsevier B.V.
The definitive version is available at: http://www.sciencedirect.com/science/article/pii/S0022039615006646
Full citation: LeCrone, Jeremy, and Gieri Simonett. "On the Flow of Non-Axisymmetric Perturbations of Cylinders via Surface Diffusion." Journal of Differential Equations 260, no. 6 (March 15, 2016): 5510-5531. doi: 10.1016/j.jde.2015.12.008.
LeCrone, Jeremy and Simonett, Gieri, "On the Flow of Non-Axisymmetric Perturbations of Cylinders via Surface Diffusion" (2016). Math and Computer Science Faculty Publications. 159.