中科院数学与系统科学研究院

数学研究所

偏微分方程研讨班

报告人：Dr. Tianxiao Huang (School of Mathematics (Zhuhai), Sun Yat-sen University)

题  目：Some unique continuation properties for higher order Schr？dinger equations

时  间：2019.11.12（星期二）, 10:00-11:00

地  点：数学院南楼N224室

摘  要：Two types of unique continuation properties for the linear higher order Schr？dinger equations will be introduced. The first type concerns unique continuation through global non-characteristic hyperplanes. I will start by reviewing some classical local theories, ideas of which may look far away from higher order evolution operators. The motivation of proving a global result comes from its possible application in non-linear problems, which was studied by Kenig, Ponce, Vega and Ionescu. The second type is quantitative. Escauriaza, Kenig, Ponce and Vega have earlier found that the Hardy’s uncertainty principle has a direct relation to a unique continuation property for Schr？dinger equations. I will introduce a result in this aspect for the higher order Schr？dinger equations in one spatial dimension, and show its sharpness by examples.