Inverse Problems for Some Nonlinear PDEs with Partial Data

Abstract

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 time-dependent Schrodinger equation. 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 analysis tools and ideas in proving injectivity of the coefficient function from its integral transforms such as the FBI transform.

About the speaker

周婷，博士毕业于美国华盛顿大学数学专业，师从国际反问题著名专家Gunther Uhlmann。先后在美国麻省理工学院数学系担任CLE Moore Instructor，美国东北大学担任副教授职位。现任浙江大学数学科学学院教授。其学术成果受到Alfred P. Sloan Foundation的肯定，于2015年被选为Alfred P. Sloan Research Fellow，两次获美国国家科学基金（NSF）数学方向的3年研究项目奖项，并于2020年荣获Simons Fellowship。