报告人：曾才斌教授 华南理工大学
时间：2024年1月11日14:30-17:30
地点：#腾讯会议：684-475-216
摘要：Little seems to be known about the invariant manifolds for SPDEs driven by nonlinear multiplicative noise. Here we contribute to this aspect and analyze the Lu-Schmalfuss conjecture on the existence of stable manifolds for a class of parabolic SPDEs driven by nonlinear multiplicative fractional noise. We emphasize that stable manifolds for SPDEs are infinite-dimensional objects, and the classical Lyapunov-Perron method cannot be applied, since the Lyapunov-Perron operator does not give any information about the backward orbit. However, by means of interpolation theory, we construct a suitable function space in which the discretized Lyapunov-Perron-type operator has a unique fixed point. Based on this we further prove the existence and smoothness of local stable manifolds for such SPDEs. This is a joint work with Xiaofang Lin and Alexandra Neamtu.
报告人介绍：曾才斌，华南理工大学教授、博士生导师、统计与金融数学系副主任，研究方向为随机微分动力系统，在JFA、JDE等学术期刊发表论文40余篇，主持承担了2项国家自然科学基金面上项目、1项国家自然科学基金天元讲习班项目、国家自然科学基金青年项目、5项省部级项目，先后学术访问犹他州立大学、赫尔辛基大学、杨百翰大学，曾获广东省优秀博士学位论文称号。

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