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A classification of solitons for the surface diffusion flow of entire graphs

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arxiv 2407.13250 v5 pith:VU7OXVVL submitted 2024-07-18 math.DG math.AP

Piotr Rybka , Glen Wheeler This is my paper · ORCID
classification math.DGmath.AP
keywords diffusionentireflowgraphssolitonssurfacearticleclassification
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In this article we classify solitons (equilibria, self-similar solutions and travelling waves) for the surface diffusion flow of entire graphs of function over the real line.

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  1. Remarks on graph-like forward self-similar solutions to the surface diffusion flow equations

    math.AP 2025-06 conditional novelty 6.0 of 10

    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.

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