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

2025/06/28 by Giga, Yoshikazu, Katayama, Sho
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.22731

Abstract

We clarify existence and non-existence of graph-like forward self-similar solutions to the planar surface diffusion equations.

Citations

• Large time behavior of exponential surface diffusion flows on ℝ
• A classification of solitons for the surface diffusion flow of entire graphs
• Stability of Self-similar Solutions to Geometric Flows
• Geometric flows with rough initial data

Related

• Stability of Self-similar Solutions to Geometric Flows
• Existence of self-similar solutions for the surface diffusion flow with nonlinear boundary conditions in the half space
• Self-similar solutions to the Navier-Stokes equations: a survey of recent results
• Forward Discretely Self-Similar Solutions of the Navier-Stokes Equations
• A classification of solitons for the surface diffusion flow of entire graphs