报告题目：Unique continuation properties for one dimensional higher order Schrodinger equations.
报 告 人： 黄山林（华中科技大学 教授）
会议时间：2021/9/13 上午7:00开始
会议地点：腾讯会议
链接：//meeting.tencent.com/dm/6grYEHHMPJei?rs=25
ID：106 472 397
报告摘要: We study two types of unique continuation properties of solutions of higher order Schrodinger equation with potential in spatial dimension one. First, considering bounded time independent potentials V(t,x)=V(x), we prove that if the solution u decays at certain exponential rate at two different times, then u=0. In particular, we show by explicit examples that our decay assumption is sharp. Second, considering time-dependent potentials V(t,x) with certain integrability, we prove that u cannot vanish on any half space of 2D spacetime plane without vanishing identically. The main ingredient of the proof is to establish a type of Lp Carleman inequality for the time dependent higher order Schrodinger operator. This is a joint work with Tianxiao Huang and Quan Zheng.
个人简介: 黄山林毕业于华中科技大学博彩导航
，现为华中科技大学博彩导航
教授，研究方向为调和分析及其在色散方程与数学控制论中的应用，主要工作发表于AJM, JFA, JDE, JGA等国际一流期刊。其在高阶薛定谔算子的唯一延拓性，流形上拉普拉斯算子的一致预解式估计，薛定谔方程的精准能控性，能观不等式等取得了系列成果，得到国际同行的广泛引用与好评。
