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报告题目：Blow-up Phenomena and Applications of Parabolic Equations Based on Nonlinear Analysis Methods
报 告 人：张玲玲，太原理工大学数学学院教授
报告摘要：This study focuses on parabolic equations with different nonlinear terms. We use the auxiliary function method, upper and lower solution method, and improved differential inequalities in nonlinear analysis to estimate the blow-up time of the equations, and achieve bidirectional regulation of blow-up suppression and induction by designing feedback control terms, so as to provide a theoretical basis for blow-up control. The variation patterns of temperature, stress and concentration of some special materials with time can be described by nonlinear parabolic equations. Therefore, the critical points of physical properties such as the material reaching the strength limit, experiencing instability or fracture, and occurring deflagration correspond to the blow-up phenomenon of the solutions. Hence, research on the blow-up and control of nonlinear parabolic equations can provide a certain theoretical basis for predicting the critical time and location of material failure.
报告人简介：张玲玲，太原理工大学数学学院教授，博士生导师，校教学委员会成员，山西省数学会常务理事，研究方向为非线性微分方程及其应用。曾于2010 年和 2017 年先后访问日本神奈川大学数学系与美国佛罗里达州立大学计算科学系。承担国家级、省部级项目十余项， 发表相关学术论文60余篇， 其中50余篇被 SCI 收录， 曾被评为山西省优秀教师、山西省中青年骨干教师， 2013年获山西省科学技术奖（自然科学类） 二等奖， 2015 年入选山西省 131 领军人才计划、山西省学术技术带头人。
报告时间：2026年4月9日（星期四）下午16:00-17:30
报告地点：长清湖校区文渊楼B536
主办单位：数学与统计学院
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