Mathematical Sciences: NSF-CBMS Regional Conference on Shock Wave Theory, June 9-13, 1997

守恒律的双曲系统在描述各种各样的物理现象中起着基本的作用，包括可压缩流体流动、磁流体动力学、反应流和多相流等。 冲击波理论的研究是重要的，因为它不仅提供了一个更好的数学理解这些复杂的现象，而且还有助于设计更强大的数值方案来解决潜在的物理问题。 与激波理论相关的主要困难是由于非线性对流引起的解的不连续特征。 对于非线性系统，理解波的相互作用是极其困难的。虽然关于解的存在性、稳定性、唯一性和渐近性已经取得了许多显著的结果，但对于系统和多维情形，仍然存在许多具有挑战性的问题。 会议的目的是为年轻的研究人员提供一个机会，系统地学习冲击波理论的最新发展。 最终目标是促进更多的研究活动，特别是在东南地区的同事中，在这个方向上。基于讲座的实质性论文应该对这一方向的未来发展产生重大影响。

Hyperbolic systems of conservation laws play fundamental roles in describing a wide variety of physical phenomena, including compressible fluid flows, magnetohydrodynamics, reacting flows, and multiphase flows, among others. The study of shock wave theory is important because it not only provides a better mathematical understanding of these complex phenomena, but also helps to design more robust numerical schemes to solve the underlying physical problems. The major difficulty associated with shock wave theory is the discontinuous feature of the solution due to the nonlinear convection. For nonlinear systems understanding the wave interactions are exceedingly hard. Although a great deal of remarkable results on the existence, stability, uniqueness and asymptotic behavior of the solution have been obtained, there are still many challenging open questions for systems and multi-dimensional cases. The goal of the meeting is to provide an opportunity for young researchers to learn systematically the recent development in shock wave theory. The ultimate goal is to promote more research activities, especially among colleagues in the southeast region, in this direction. The substantial expository paper based on the lectures should have significant influence for future development in this direction.