报告题目：Spatial dynamics and optimization method for a network propagation model in a shifting environment

报告人  ：朱霖河

报告时间：2021年1月21日（周四）下午14:00

报告地点：腾讯会议平台（会议ID: 164419982）

主办单位：南京邮电大学自动化学院，人工智能学院、江苏省自动化学会

报告人简介：朱霖河，理学博士，江苏大学硕士生导师，美国《数学评论》（Mathematical Reviews）特约评论员，2016-2017年美国亚利桑那州立大学访问学者，主要研究方向包括动力系统理论、网络传播动力学分析与控制等，以第一作者身份在Information Sciences、Journal of Nonlinear Science、Discrete and Continuous Dynamical Systems、Chaos、Applied Mathematical Modelling等期刊发表SCI检索论文约30篇（ESI高被引论文1篇），发表北大核心期刊教学论文1篇，主持国家自然科学基金青年项目、江苏省自然科学基金青年项目、中国博士后科学基金面上项目和江苏省高校自然科学基金面上项目各一项，获江苏省高等学校自然科学奖二等奖、南京航空航天大学科学技术进步奖三等奖、南京航空航天大学“群星”创新奖各一项，近两年指导研究生和本科生数学建模竞赛获美国（国际）特等奖提名奖（Finalist奖）、全国二等奖、江苏省一等奖、二等奖和三等奖30余项，指导学生获省级大创项目1项。

报告摘要：In this work, a reaction-diffusion rumor propagation model with general incidence rate is proposed in a spatially heterogeneous environment. We first summarize the well-posedness of global solutions. Then the basic reproduction number R0 is introduced for the model which contains the spatial homogeneity as a special case. The threshold-type dynamics are established in terms of R0, including the global asymptotic stability of the rumor-free steady state and the uniform persistence of all positive solutions. Furthermore, by applying a controller to this model, we investigate the optimal control problem. Employing the operator semigroup theory, we prove the existence, uniqueness and some estimates of the positive strong solution to the controlled system. Subsequently, the existence of the optimal control strategy is established with the aid of minimal sequence techniques and the first order necessary optimality conditions for the optimal control is deduced. Finally, some numerical simulations are performed to validate the main analysis.