Dr. Tianxiao Huang: Some unique continuation properties for higher order Schrodinger equations

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Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Dr. Tianxiao Huang，School of Mathematics (Zhuhai), Sun Yat-sen University
Inviter:
Title:	Some unique continuation properties for higher order Schrodinger equations
Time & Venue:	2019.11.12 10:00-11:00 N224
Abstract:	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 Schrodinger equations. I will introduce a result in this aspect for the higher order Schrodinger equations in one spatial dimension, and show its sharpness by examples.