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

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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.