On the surface diffusion flow

Joachim Escher, Uwe F. Mayer, Gieri Simonett

Abstract: In this paper we present recent existence, uniqueness, and stability results for the motion of immersed hypersurfaces driven by surface diffusion. We provide numerical simulations for curves and surfaces that exhibit the creation of singularities. Moreover, our numerical simulations show that the flow causes a loss of embeddedness for some initially embedded configurations.

Key words:Numerical simulation, surface diffusion, mean curvature, gradient flow, free boundary problem, immersed hypersurface.

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