The scattering theory has been an attractive topic in mathematical physics over a hundred years. It explains many physical phenomena such as the blue sky, or the diffraction of particles. Modern technologies, such as the medical imaging and the radar, are developed with the help of the mathematical theory of direct and inverse scattering problems. Roughly speaking, the scattering theory concerns the behaviour of an incident particle or wave when it meets an inhomogeneous medium, which is always governed by partial differential equations. The direct scattering problem is to study the well-posedness of the equations from theoretical and numerical point of view. When the solution can be measured at some points but some parameters in the PDE are unknown, the process to reconstruct these parameters is called the inverse scattering problem. In this seminar, we will discuss several mathematical tools to study the direct and inverse scattering problems, which are listed as follows.
- Integral equation method
- Variational method
- Uniqueness of inverse scattering problems
- Tikhonov regularization for ill-posed problems
- Iterative method to solve inverse problems
- Linear sampling method for inverse scattering problems
- Trainer/in: Hans-Christian Kreusler
- Trainer/in: Julia Wilton
- Trainer/in: Ruming Zhang