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. | | | |