Self-intersections for the surface diffusion and the volume-preserving mean curvature flow

We prove that the surface diusion ow and the volume preserving mean curvature ow can drive embedded hypersurfaces to self-intersections.

[1]  G. Huisken.  The volume preserving mean curvature flow. , 1987 .

[2]  L. Bronsard,et al.  Volume-preserving mean curvature flow as a limit of a nonlocal Ginzburg-Landau equation , 1997 .

[3]  J. Escher,et al.  The surface diffusion flow for immersed hypersurfaces , 1998 .

[4]  J. Taylor,et al.  Overview no. 113 surface motion by surface diffusion , 1994 .

[5]  Giuseppe Da Prato,et al.  Equations d'évolution abstraites non linéaires de type parabolique , 1979 .

[6]  U. Mayer.  Numerical solutions for the surface diusion ow in three space dimensions , 2001 .

[7]  W. Mullins.  Theory of Thermal Grooving , 1957 .

[8]  J. Duchon,et al.  Evolution D'une Interface par diffusion de surface , 1984 .

[9]  M. Gage.  On an area-preserving evolution equation for plane curves , 1986 .

[10]  J. Escher,et al.  ON THE SURFACE DIFFUSION FLOW , 2000 .

[11]  Andrea L. Bertozzi,et al.  Axisymmetric Surface Diffusion: Dynamics and Stability of Self-Similar Pinchoff , 1998 .

[12]  Herbert Amann,et al.  Linear and Quasilinear Parabolic Problems , 2019, Monographs in Mathematics.

[13]  Charles M. Elliott,et al.  The Cahn–Hilliard equation with a concentration dependent mobility: motion by minus the Laplacian of the mean curvature , 1996, European Journal of Applied Mathematics.

[14]  Morton E. Gurtin,et al.  On the motion of a phase interface by surface diffusion , 1990 .

[15]  Yoshikazu Giga,et al.  On pinching of curves moved by surface diffusion , 1997 .

[16]  Richard S. Falk,et al.  Space-Time Finite Element Methods for Surface Diffusion with Applications to the Theory of the Stability of Cylinders , 1996, SIAM J. Sci. Comput..

[17]  J. Escher,et al.  The volume preserving mean curvature flow near spheres , 1998 .

[18]  Sigurd B. Angenent,et al.  Nonlinear analytic semiflows , 1990, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.