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

双曲型守恒定律在描述各种物理现象方面起着重要的作用，包括可压缩流体流动、磁流体动力学、反应流动和多相流等等。激波理论的研究非常重要，因为它不仅提供了对这些复杂现象的更好的数学理解，而且有助于设计更稳健的数值格式来解决潜在的物理问题。激波理论的主要困难在于非线性对流引起的解的不连续性。对于非线性系统来说，理解波的相互作用是非常困难的。虽然在解的存在性、稳定性、唯一性和渐近性方面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开放问题。会议的目的是为年轻的研究人员提供一个机会，系统地了解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，朝着这个方向。以讲座为基础的实质性说明性论文将对今后在这一方向上的发展产生重大影响。

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.