Remarks on Graph-Like Forward Self-Similar Solutions to the Surface Diffusion Flow Equations

Key Points

• This research aims to clarify the conditions under which graph-like forward self-similar solutions exist for surface diffusion equations.
• Theoretical analysis of surface diffusion flow equations
• Existence and non-existence proofs
• Examination of self-similarity in solutions
• Conditions for the existence of graph-like self-similar solutions are established
• Certain parameters lead to non-existence of such solutions