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MS20 2: Recent advances in inverse problems for elliptic and hyperbolic equations
Time:
Thursday, 07/Sept/2023:
4:00pm - 6:00pm
Session Chair: Ru-Yu Lai
Location:VG3.104
Presentations
Fixed angle inverse scattering for velocity
Rakesh Rakesh
University of Delaware, United States of America
An inhomogeneous acoustic medium is probed by a plane wave and the resultant time dependent wave is measured on the boundary of a ball enclosing the inhomogeneous part of the medium. We describe our partial results about the recovery of the velocity of the medium from the boundary measurement. This is a formally determined inverse problem for the wave equation, consisting of the recovery of a non-constant coefficient of the principal part of the operator from the boundary measurement.
Inverse Problems for Some Nonlinear Schrodinger Equations
Ting Zhou
浙江大学, China, People's Republic of
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.
