报告题目：Averaging method for initial and boundary value problems of set-valued differential equations with maxima

报告人：王培光教授(河北大学)

报告时间：2025年4月09日(10:30-11:30)

报告地点：复杂系统研究所四层(409室)

报告人简介：王培光，河北大学数学与信息科学学院教授，博士生导师，河北大学坤舆学者。主要从事微分方程的定性与稳定性理论，非线性系统控制，系统分析与决策和应用课题的研究工作。先后荣获全国优秀百篇博士论文提名奖，第六届全国高等院校霍英东青年教师奖，第六届全国高等院校优秀教学成果二等奖，河北省自然科学二等奖，河北省科技进步二等奖，河北省自然科学三等奖等10余项省部级奖励。荣获河北省教学名师、河北省优秀科技工作者等荣誉称号。

报告人摘要：In this talk, we investigate the asymptotic approximation of solutions of initial and boundary value problems for set-valued differential equations with maxima. Set-valued differential equations is one of the generalized forms of differential system, which can more accurately describe the motion trajectory of objects. It can also be used to study set-valued differential inclusions, fuzzy differential equations and other problems. However, due to the complexity of the set-valued differential equations itself, it is difficult to find its exact solution. In this paper, by using the averaging method, we mainly study the following set-valued differential equations with maxima. It is noted that the known results on the averaging method of set-valued differential equations are mostly in the case of the existence of the average limit of the right-hand function, it is rare to deal with that the averaging method for set-valued differential equations with right-hand side for the case when the limit of a method of an average does not exist. By introducing the concepts of Hausdorff measure and semideviation measure, the approximate relationship of the solutions between the original equations and the average equations is discussed via the averaging method when the average limit of the right-hand function exists or does not exist.

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