The self-similar expanding curve for the curvature flow equation. (English) Zbl 1032.35084
The aim of this paper is to investigate a two point boundary value problem for the mean curvature flow equation. It leads to a Neuman boundary value problem for a nonlinear parabolic equation in non-divergence form. They study self-similar solutions for which existence and uniqueness theorems are obtained. Furthermore, they investigate dynamic stability of a self-similar expanding curve.
Reviewer: Daniel Ševčovič (Bratislava)
MSC:
35K55 | Nonlinear parabolic equations |
53C44 | Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010) |
35B35 | Stability in context of PDEs |