Uniqueness of self-similar solutions to the network flow in a given topological class
Uniqueness of self-similar solutions to the network flow in a given topological class
复制标题
给定拓扑类中网络流自相似解的唯一性
DOI：
10.1080/03605302.2010.539892
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Mariel S'aez Trumper
中科院分区：
文献类型：
--
作者：
Mariel S'aez Trumper
本文研究了网络流在固定拓扑类中扩张自相似解的唯一性。我们证明的结果通过抛物Allen-Cahn近似证明在\cite{triodginz}。
此外，我们还证明了连通树型网络的任何正则演化（初始条件可能不是正则的）在给定的拓扑类中是唯一的。
In this paper we study the uniqueness of expanding self-similar solutions to the network flow in a fixed topological class. We prove the result via the parabolic Allen-Cahn approximation proved in \cite{triodginz}.
Moreover, we prove that any regular evolution of connected tree-like network (with an initial condition that might be not regular) is unique in a given a topological class.