Inverse Problems for Some Nonlinear Partial Differential Equations

Abstract

In this talk, the speaker will demonstrate the higher order linearization approach to solve several inverse boundary value problems for nonlinear partial differential equations, 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. She will focus the 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.

References:
[1] R.-Y. Lai and T. Zhou, Inverse problems for nonlinear fractional magnetic Schrödinger equation, submitted, arXiv:2103.08180.
[2] R.-Y. Lai and T. Zhou, Partial data inverse problems for nonlinear magnetic Schrödinger equation, accepted by Math. Res. Lett., arXiv:2007.02475.

About the Speaker

Prof. ZHOU Ting received her PhD in Mathematics at the University of Washington in 2010. She was a C.L.E. Moore Instructor at the Massachusetts Institute of Technology in 2011-2014, after which she held an Associate Professor position at Northeastern University until 2021. She joined Zhejiang University in 2022 and is currently a Professor of Mathematics there.

Prof. Zhou’s research interests include partial differential equations, inverse problems for linear and nonlinear differential equations and transformation-optics based design of invisibility and cloaking. She was awarded Sloan Research Fellowship in 2015 and Simons Fellowship in 2020.

For Attendees' Attention

This talk will be held online via Zoom. To attend, please join the Zoom meeting at https://hkust.zoom.us/j/95343046659 (Meeting ID: 953 4304 6659 / Passcode: iasip2022).

About the Program

For more information, please refer to the program website at https://iasprogram.hkust.edu.hk/inverseproblems/.