350vip8888新葡的京集团350vip8888新葡的京集团2024年第36期数理大讲堂

报告人：Prof. Tomás Caraballo， Universidad de Sevilla, Spain

报告时间：2024年12月16日上午8：20—9：20

地点：350vip8888新葡的京集团3号楼 3B205

主持人：赵才地教授

报告人简介：Prof. Tomás 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，主要研究随机偏微分方程吸引子的存在性和内部结构，随机动力系统等。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。

报告题目： Recent results on non-local deterministic andstochastic models

(inspired by Michel Chipot's work)

报告摘要：The aims of this talk is to report on some recent resultson non-local partial di_erential equations (both deterministic and stochas-tic) that have been obtained, by our research group during the last decade, and which are inspired in the nice investigation that Michel chipot and his collaborators had previously carried out from the 90's on. First of all, we were able to analyse non-local non-autonomous reaction-di_usion equations by exploiting the techniques of pullback attractors, which has proven very appropriate for the asymptotic behavior of non-autonomous dynamical systems. Next, we considered non-local problems containing some hereditary

characteristics (delay, memory), and performed a complete analysis concerning well-posedness, local stability, and global stability (existence of attrac-tors). A model concerned with non-local di_usion and memory deserves a special treatment since we could establish the appropriate framework for studying its asymptotic behavior, instead of the one provided by Dafermo's transformation which usually had been used for this kind of problems. But also, we have analyzed the more realistic models containing some kind of randomness or stochasticity. We have developed a theory for the treatment

of non-local models containing di_erent kinds of noise, and have made use of the powerful theories of random dynamical systems, mean weak random attractors, approximation by colored noise, etc to obtain interesting properties about the differences with the deterministic counterparts. Our deepest thanks to Michel for having been the inspiration of a fruitful research line of our research group.