题目：Partially dissipative hyperbolic systems with time-dependent damping

报告人：朱启孟，巴黎高等师范学院（École normale supérieure）

时间：2026年3月4日（星期三）14:00-15:30

地点：东区第五教学楼5107教室

摘要：We consider quasilinear partially dissipative hyperbolic systems with time-dependent damping in the whole space~$\R^d$, with~$d \ge 1$. 

Using an approach similar to that developed by Crin-Barat and Danchin, we establish the global existence of small-amplitude solutions for systems endowed with a damping term of the form  $-\frac{K z}{(1+t)^{\alpha}}, \qquad 0 < \alpha \le 1.$

We assume that the linearized system satisfies the Shizuta--Kawashima (SK) condition, which ensures that the dissipation acts on all characteristic components through coupling. 

The key idea is to construct a Lyapunov-type functional that compensates for the lack of full dissipation. Such a functional was first introduced by Beauchard and Zuazua in the framework of control theory.

报告人简介：朱启孟，巴黎高等师范学院（École normale supérieure）博士生，中法数学英才班2019级学生。