Existence and uniqueness of the motion by curvature of regular networks

Interfaces and free boundaries

article

Michael Gößwein¹  Julia Menzel²  Alessandra Pluda³ 

[1] Universität Duisburg-Essen;Universität Regensburg;Università di Pisa

关键词: Networks;    motion by curvature;    local existence and uniqueness;    parabolic regularisation;    non-linear boundary conditions;    long-time existence;   

DOI  :  10.4171/ifb/477

学科分类：生物化学工程

来源: European Mathematical Society

【 摘 要 】

We prove existence and uniqueness of the motion by curvature of networks with triple junctions in Rd\mathbb{R}^dRd when the initial datum is of class Wp2−2/pW^{{2-{2}}/{p}}_pWp2−2/p​ and the unit tangent vectors to the concurring curves form angles of 120120120 degrees. Moreover, we investigate the regularisation effect due to the parabolic nature of the system. An application of the well-posedness is a new proof and a generalisation of the long-time behaviour result derived by Mantegazza et al. in 2004. Our study is motivated by an open question proposed in the 2016 survey from Mantegazza et al.: does there exist a unique solution of the motion by curvature of networks with initial datum being a regular network of class C2C^2C2? We give a positive answer.

【 授权许可】

CC BY