报 告 人：周 军 教授（西南大学）
报告题目：Infinite time blow-up of solutions to a class of wave equations with weak and strong damping terms and logarithmic nonlinearity
报告时间：2021年6月29日（周二）上午10:00-11:00
报告地点：静远楼1506学术报告厅
报告人简介：
周军，西南大学数学与统计学院教授，博士研究生导师。1981年8月出生，四川成都人。2011年在重庆大学获博士学位，2012年-2013年，美国威廉玛丽学院访问学者。重庆市高校青年骨干教师，重庆市数学学会理事，担任美国“数学评论”评论员。先后主持了国家级省部级项目5项，主持了中央高校基本科研业务费一般项目，重点项目，重大项目各一项。主要研究方向包括：（1）偏微分方程与无穷维动力系统；（2）非线性反应扩散方程与模式生成。在《J. Differential Equations》、《Nonlinearity》、《J. Nonlinear Science》、《中国科学》等国内外重要期刊上发表学术论文120余篇，其中SCI收录120余篇。
报告摘要：
This talk investigates the infinite time blow-up of solutions with arbitrary high initial energy to wave equations with weak damping term, strong damping term, and logarithmic nonlinearity. This problem has been studied previously with the assumptions that there is no strong damping term and the initial displacement and initial velocity have the same sign. However, from the physical point of view, it is obvious that the initial displacement and initial velocity may have different signs, and it is very necessary to consider the effects of the strong damping term. For example, the strong damping term indicates that the stress is not only proportional to the strain as with the Hooke law, but also proportional to the strain rate as in a linearized Kelvin–Voigt material. In this paper, by providing a completely different method from previous studies, we show that the solutions may blow up at infinity with arbitrary high initial energy when the model involves the strong damping term and the initial displacement and initial velocity may have different signs. Moreover, in this paper, we prove for the first time how to extend the solution over time (the whole half line) in studying the infinite time blow-up phenomena for hyperbolic equations with logarithmic nonlinearity. These results fill in the gaps in previous studies on this type of models.
邀 请 人：彭 锐