报告题目：Recent trends on non-local deterministic and stochastic models

报告人：Tomá‌s Caraballo, Universidad de Sevilla

邀请人：黎定仕

时间：10月15日（周四）上午10: 40-11: 40

地点：X9136

摘要：The aims of this talk is to report on some recent results on non-local partial differential equations (both deterministic and stochastic) 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-diffusion 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 attractors). A model concerned with non-local diffusion 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 different 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.

个人简介：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，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340余篇，并著有《Applied Nonautonomous and Random Dynamical Systems》,《Applied Dynamical Systems》等专著。

主办： av解说

av解说 数学中心