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On Well-Posedness, Stability, And Bifurcation For The Axisymmetric Surface Diffusion Flow, Jeremy Lecrone, Gieri Simonett
On Well-Posedness, Stability, And Bifurcation For The Axisymmetric Surface Diffusion Flow, Jeremy Lecrone, Gieri Simonett
Department of Math & Statistics Faculty Publications
We study the axisymmetric surface diffusion (ASD) flow, a fourth-order geometric evolution law. In particular, we prove that ASD generates a real analytic semiflow in the space of (2+α)-little-Holder regular surfaces of revolution embedded in R3 and satisfying periodic boundary conditions. Further, we investigate the geometric properties of solutions to ASD. Utilizing a connection to axisymmetric surfaces with constant mean curvature, we characterize the equilibria of ASD. Then, focusing on the family of cylinders, we establish results regarding stability, instability, and bifurcation behavior, with the radius acting as a bifurcation parameter.