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)

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

  间:2019.11.12(星期二), 10:00-11:00

  点:数学院南楼N224

 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.

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