Tai-Ping Liu 教授 & Seung Yeal Ha 教授 特別講演会

There have been continuing progresses in shock wave theory for the past half century. Deep results are obtained for one-dimensional conservation laws. Some of the central issues that have been raised and resolved are the entropy condition, Riemann problem, N-waves, compactness and regularity due to nonlinearity, well-posedness, and zero dissipation limits.

In recent years, there are focused and intensive efforts on the study of multi-dimensional shock waves in gas flows. This is to go back to the basic physical concerns of people like Prandtl and von Neumann in the first half of 20th century, as recorded in the classical book of Courant-Friedrichs. However, the classical works are mostly about shock polar and simple waves and are algebraic in nature. The recent efforts aim at solving nonlinear partial differential equations of mixed types with free boundary. Because of the obvious mathematical difficulties, it is important to identify basic physical problems, in particular the role played by the solid boundary.

We will survey the historical developments, discuss the recent efforts, and raise open problems.