Partially dissipative hyperbolic systems with time-dependent damping
数学专题报告
报告题目(Title)：Partially dissipative hyperbolic systems with time-dependent damping
报告人(Speaker)：Dr. Qimeng Zhu (Université Paris-Est Créteil, France)
地点(Place)：Zoom ID: 894 976 18264 Password: 123456
时间(Time)：2026年3月20日（周五）16:00-17:00
邀请人(Inviter)：薛留堂
报告摘要
We consider quasilinear partially dissipative hyperbolic systems with time-dependent damping in the whole space R^d, with d ≥ 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 - K z / (1+t)^α, 0 < α ≤ 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.
