报告题目：Dynamical systems generated by pantograph differential equations  

报 告 人：Tomas Caraballo, Universidad de Sevilla, Spain

报告时间：2026年03月19日（星期四）14:00-15:00

报告地点：7JC214

报告摘要：This talk is concerned with the pantograph delay differential equation on R^d (d>1) with initial time t_0∈R. First, the global wellposedness of the solution is proved. Then, a two-parameter semigroup on the weighted space C_{γ_0}(R^−, R^d) is constructed, which is not formed naturally from the well-posedness of the solution due to the peculiarities of the delay term in the pantograph system. Finally, the existence of a pullback attractor and a forward attractor is established by the existence of a compact set which is uniformly attracting for the two-parameter semigroup associated to the system. The analysis of pantograph equations requires a non-autonomous set-up due to the special nature of the proportional delay, and remained as an open problem for more than 20 years. Thanks to a nice interpretation of the delay terms, we were able to handle the problem in an appropriate framework.

报告人简介：Tomas Caraballo，西班牙塞维利亚大学终身教授，博士生导师，美国奥本大学客座教授。主要研究领域是随机偏微分方程和泛函微分方程。先后在Comm. PDE, SIAM J. Math. Anal., J. Differential Equations, Proc. AMS, J. Dynam. Differential Equations, SIAM Appl. Dyn. Syst.等数学权威期刊上发表论文三百四十余篇，并著有《Applied Nonautonomous and Random Dynamical Systems, Applied Dynamical Systems》，多次受邀在华中科技大学、华南理工大学，西北大学、东华大学等学术访问并做报告。