讲座题目：Global existence, blowup phenomena, and asymptotic behavior for quasilinear Schrodinger equations

主讲人：宋先发 副教授 （天津大学）

主持人：陈秀卿 教授

时间：2019年1月2日（周三）上午11:00-12:00

地点：主楼1214

主要内容：

In this paper, we deal with the Cauchy problem of the quasilinear Schrodinger equation iu_t = ∆u + 2uh′ (|u| 2 )∆h(|u| 2 ) + F(|u| 2 )u for x ∈ R^N , t > 0 u(x, 0) = u0(x), x ∈ R^N . Here h(s) and F(s) are some real-valued functions, with various choices for models from mathematical physics. We examine the interplay between the quasilinear effect of h and nonlinear effect of F for the global existence and blowup phenomena. We provide sufficient conditions on the blowup in finite time and global existence of the solution. In some cases, we can deduce the watershed from these conditions. In the focusing case, we construct the sharp threshold for the blowup in finite time and global existence of the solution and lower bound for blowup rate of the blowup solution. Moreover, we establish the pseudo-conformal conservation law and some asymptotic behavior results on the global solution

主讲人简介：

宋先发副教授，2003年大连理工大学取得博士学位，2004年至2006年清华大学数学科学系博士后，2008年至今担任天津大学数学学院副教授。研究方向是偏微分方程定性理论。