报告人：许勇 (西北工业大学)

报告题目：Averaging principles for non-autonomous slow-fast systems of stochastic reaction-diffusion equations with jumps

报告摘要: We are devoted to developing the averaging principle for non-autonomous systems of reaction-diffusion equations driven by Poisson random measures. The coefficients of the fast equation depend on time, and some of them are periodic or almost periodic. So, the classical formulation of the averaging principle to proving the invariant measure of the fast equation is no longer available. For this reason, the existence of time-dependent evolution family of measures associated with the fast equation is studied, and proved that it is almost periodic. Next, using the characteristics of almost periodic function, the averaged coefficient is defined by the evolution family of measures. Then, the averaged equation is given. Finally, using the classical Khasminskii method, we prove the validity of the averaging principle.

报告人简介：许勇，西北工业大学教授、博导、优秀青年教师，曾任理学院应用数学系主任。主要研究方向为非线性与随机动力学。在列维噪声作用下非线性动力学系统的跃迁现象、随机动力学系统的稳定性分析与近似解析方法、分数高斯噪声下的平均理论等三个方面取得了创新性成果，并成功应用于深水海洋管线监测、水下弱目标探测及水下保密通信等重要实际工程问题。2011 年以来已在国内外著名期刊上发表 SCI 源期刊论文 57 篇（SCI 收录 54 篇），其中第一作者31 篇。研究成果以第1完成人分别获得2016年教育部高等学校自然科学二等奖和2016年陕西省科学技术一等奖。

报告时间：2018年10月18日（星期四）上午11:00-12:00

报告地点：科技楼南楼702