报告时间：9月20日9：00-11：00
报告地点：11-105
报告人：Tomas Caraballo
题目：Dynamics of infinite-dimensional systems with memory
摘要：
In this talk, the asymptotic behavior of a semilinear heat equation as well as a damped wave equation containing long time memory are analyzed. We set up the problems in the usual framework for dynamical systems generated by differential equations with delay terms. This approach is different from the previous published literature on the long time behavior of heat and wave equations with memory, which were investigated in an extended space after having used the well-known Dafermos transformation. As a consequence, the obtained results provide complete information about the attracting sets for the original problem, instead of the transformed extended one (see [1, 2]).
References
[1] S. Yan, J.H. Xu, T. Caraballo, J. Valero, Dynamics of damped wave equations with long time memory, Commun. Nonlinear Sci. Numer. Simul. 156 (2026), Paper No. 109631
[2] J.H. Xu, T. Caraballo, J. Valero, Asymptotic behavior of a semilinear problem in heat conduction with long time memory and non-local diffusion. J. Differential Equations 327 (2022), 418–447
报告人简介：
Tomas Caraballo教授，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，国际上无穷维动力系统和随机动力系统领域的著名专家。先后在Math Ann., Comm. PDE, SIAM J. Math Anal., J. Diff. Equations, Proc. AMS, 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》等专著。
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江苏理工学院数理学院