Nonparametric mean curvature type flows of graphs with contact angle conditions

2017/02/08 by Hengyu Zhou, Zhou, Hengyu
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1702.02449

openalex publication_date 2017/02/08 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

In this paper we study nonparametric mean curvature type flows in M×ℝ which are represented as graphs (x,u(x,t)) over a domain in a Riemannian manifold M with prescribed contact angle. The speed of u is the mean curvature speed minus an admissible function ψ(x,u,Du). Long time existence and uniformly convergence are established if ψ(x,u, Du)≡ 0 with vertical contact angle and ψ(x,u,Du)=h(x,u)ω with h_u(x,u)≥ h₀>0 and ω=√(1+|Du|²). Their applications include mean curvature type equations with prescribed contact angle boundary condition and the asymptotic behavior of nonparametric mean curvature flows of graphs over a convex domain in M² which is a surface with nonnegative Ricci curvature.

Citations

• On capillary free surfaces in a gravitational field
• Mean Curvature Flows of Graphs with Neumann Boundary condition

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