Excess action and broken characteristics for Hamilton-Jacobi equations
Excess action and broken characteristics for Hamilton-Jacobi equations
复制标题
DOI：
10.1016/j.na.2014.08.001
复制
发表时间：
2014-11-01
影响因子：
1.4
通讯作者：
Ahmadzadeh, Farzaneh
中科院分区：
文献类型：
--
作者：
Stromberg, Thomas;Ahmadzadeh, Farzaneh
本文利用超额拉格朗日作用量和相关的一类特征，研究了Hamilton-Jacobi方程S-t + H（t，x，delS）= 0，（t，x）是（0，无穷大）xR-n中的一个元素的奇性传播.在某种意义上，过量作用量测量曲线X（t）对于给定的哈密顿-雅可比方程的粘性解S（t，x）离作用量最小化有多远。断裂特征被定义为曲线沿着，多余的动作以尽可能慢的速度增长。特别是，我们证明了破碎的特性进行的奇异性的粘度解决方案。(C)2014 Elsevier Ltd.
We study propagation of singularities for Hamilton-Jacobi equationsS-t + H(t, x, del S) = 0, (t, x) is an element of(0, infinity) x R-n,by means of the excess Lagrangian action and a related class of characteristics. In a sense, the excess action gauges how far a curve X(t) is from being action minimizing for a given viscosity solution S(t, x) of the Hamilton-Jacobi equation. Broken characteristics are defined as curves along which the excess action grows at the slowest pace possible. In particular, we demonstrate that broken characteristics carry the singularities of the viscosity solution. (C) 2014 Elsevier Ltd.