学术报告（于东晓 10.9）

摘要：

I will discuss the modified scattering theory for a scalar quasilinear wave equation in three space dimensions. This equation satisfies the weak null condition, and it admits a global solution for sufficiently small $C_c^\infty$ data. To describe the asymptotic behavior of a global solution, we first identify a new notion of asymptotic profile by deriving a new reduced system for our model equation. We then discuss both the existence of the modified wave operators and asymptotic completeness for the model equation. I will also talk about a related work on the construction of nontrivial global solutions to some 3D quasilinear wave equations.