中科院数学与系统科学研究院

数学研究所

学术报告

调和分析和偏微分方程研讨班

报告人： 周婷 （浙江大学）

题  目：Inverse Problems for Some Nonlinear PDEs

时  间：2022.05.31（星期二）17:00-18:00

地  点：腾讯会议 633-263-251

摘  要：In this talk, I will demonstrate the higher order linearization approach to solve several inverse boundary value problems for nonlinear PDEs, modeling for example nonlinear optics, including nonlinear magnetic Schrodinger equation and its fractional version. Considering partial data problems, the problem will be reduced to solving for the coefficient functions from their integrals against multiple linear solutions that vanish on part of the boundary. We will focus our discussion on choices of linear solutions and some microlocal anlaysis tools and ideas in proving injectivity of the coefficient function from its integral transforms such as the FBI transform.