题目：Hyperbolicity, resonances, instabilities
报告人：Benjamin Texier, University of Paris 7.
摘要: We discuss local-in-time well-posedness for the Cauchy problem for first-order systems of quasi-linear partial differential equations, with a particular eye towards ill-posed systems. In the symmetric case, the famous theorem of Friedrichs-Kato-Lax implies well-posedness. In the opposite direction, the theorems of Lax-Mizohata-Metivier show that hyperbolicity is necessary for well-posedness. We will discuss extensions of the Lax-Mizohata-Metivier theory, and uses of the symbolic flow method to exhibit instabilities. Collaborators include Eric Dumas (Grenoble), Nicolas Lerner (Paris), Lu Yong (Nanjing) and Toan Nguyen (Penn State).