The Level Set Method for Systems of PDEs
The Level Set Method for Systems of PDEs
复制标题
偏微分方程组的水平集方法
DOI：
10.1080/03605300600910407
复制
发表时间：
2007
影响因子：
1.9
通讯作者：
M. Novaga
中科院分区：
文献类型：
--
作者：
G. Bellettini;H. Chermisi;M. Novaga
我们提出了一种求解偏微分方程组的水平集方法，该方法与Evans（1996）对热方程以及Giga和Sato（2001）对Hamilton-Jacobi方程的研究是一致的。我们的方法如下几何结构的概念引入的障碍德Giorgi。其主要思想是强制不同余维流形之间的比较原则，并要求水平集方程的解的每个非零子水平是相应系统的解的图的障碍。本文将此方法应用于一类一阶拟线性方程组。我们计算水平集方程与适当的一阶系统的守恒律，与平均曲率流的流形的任意余维和系统的反应扩散方程。
We propose a level set method for systems of PDEs which is consistent with the previous research pursued by Evans (1996) for the heat equation and by Giga and Sato (2001) for Hamilton–Jacobi equations. Our approach follows a geometric construction related to the notion of barriers introduced by De Giorgi. The main idea is to force a comparison principle between manifolds of different codimension and require each nonzero sub-level of a solution of the level set equation to be a barrier for the graph of a solution of the corresponding system. We apply the method to a class of systems of first order quasi-linear equations. We compute the level set equation associated with suitable first order systems of conservation laws, with the mean curvature flow of a manifold of arbitrary codimension and with systems of reaction–diffusion equations.