本项目拟研究一类守恒系统（非严格双曲系统）大粘性激波长时间性态问题。我们旨在通过该项目的研究，发展一个新的研究框架（分离框架），去掉前人在研究激波结构问题时对其大小的限制。具体地，我们将利用该框架把远场的双曲波结构与局部波前结构分离开来，给出一般激波附近线性化系统初值问题基本解的逐点结构; 并且进一步通过分析非线性波相互作用的过程，给出原系统对初始激波小扰动的非线性稳定性结论以及逐点收敛速率。

In this project, we are preparing to consider the long time behavior of strong shock profile for a non-strictly hyperbolic conservation laws. Our aim is to develop a new method (split scheme) so that we can give the structure of shock profile without the small assumption. More specifically, we will use our scheme to give the pointwise structure of the initial problem for the linearized system around the general shock profile by separating the hyperbolic wave structure in the far fields and local structure around shock front. We also try to prove the nonlinear stability of the shock profile against small perturbations with a pointwise convergent rate, through the local study of the nonlinear wave interactions.