Remarks on graph-like forward self-similar solutions to the surface diffusion flow equations
Yoshikazu Giga, Sho Katayama
TL;DR
This paper investigates the existence and non-existence of graph-like forward self-similar solutions to planar surface diffusion equations, clarifying conditions under which such solutions can or cannot occur.
Contribution
It provides new insights into the conditions for the existence of self-similar solutions in surface diffusion flow, addressing gaps in previous research.
Findings
Identifies conditions for existence of solutions
Establishes non-existence results under certain conditions
Clarifies the mathematical structure of self-similar solutions
Abstract
We clarify existence and non-existence of graph-like forward self-similar solutions to the planar surface diffusion equations.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Geometric Analysis and Curvature Flows · Navier-Stokes equation solutions