On curvature flow with driving force under Neumann boundary conditon in the plane

2017/03/30 by Longjie Zhang, Zhang, Longjie
Computer Science · Mathematics · #35A01 #35A02 #35K55 #53C44 #Advanced Mathematical Modeling in Engineering #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1703.10707

openalex publication_date 2017/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a family of axisymmetric curves evolving by its mean curvature with driving force in the half space. We impose a boundary condition that the curves are perpendicular to the boundary for t>0, however, the initial curve intersects the boundary tangentially. In other words, the initial curve is oriented singularly. We investigate this problem by level set method and give some criteria to judge whether the interface evolution is fattening or not. In the end, we can classify the solutions into three categories and provide the asymptotic behavior in each category. Our main tools in this paper are level set method and intersection number principle.

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