For the planar surface diffusion flow, small V-shaped data produce genuine nonlinear forward self-similar graph solutions, while a growth condition forces any profile to be a line.
Asian J.\ Math.\ 16 (2012), 209--235
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Remarks on graph-like forward self-similar solutions to the surface diffusion flow equations
For the planar surface diffusion flow, small V-shaped data produce genuine nonlinear forward self-similar graph solutions, while a growth condition forces any profile to be a line.