粘性解是由Crandall与Lions于1983年引入的一种偏微分方程弱解的概念。粘性解的不可微点称为奇点，奇点的传播问题一直备受关注。本项目旨在研究一类一阶偏微分方程（GHJ）粘性解的奇性传播问题。这类偏微分方程的特征线方程是接触Hamilton系统。我们的方法来源于动力系统。具体地，本项目将围绕以下三个问题进行研究：1.方程（GHJ）粘性解奇性（全局）传播的充分必要条件；2.方程（GHJ）粘性解奇点集的拓扑结构；3.方程（GHJ）的不同粘性解的奇性传播之间的关系以及奇性传播的曲面问题。

The notion of viscosity solutions was introduced by Crandall and Lions in 1983, which is a kind of weak solutions of partial differential equations. The points at which the viscosity solution fails to be differentiable are called singular points. The problem of propagation of singularities is always highly focused on. The project focuses on the problem of propagation of singularities of viscosity solutions of a class of first-order partial differential equations (GHJ). The characteristic equations for this class of partial differential equations are contact Hamiltonian systems. Our method originates from dynamical systems. More precisely, we will discuss the following three problems: 1. the necessary and sufficient conditions for (global) propagation of singularities of viscosity solutions of equation (GHJ); 2. the topology of the set of singularities of viscosity solutions of equation (GHJ); 3. the relationship between propagations of singularities for different viscosity solutions of equation (GHJ) and the problem of propagation of singularities along surfaces.