Joint BCAM-UPV/EHU Analysis and PDE seminar: Uniqueness and numerical reconstruction for inverse problems dealing with interval size search

Abstract

In recent years, the interest in the analysis and solution of inverse problems of many kinds has grown a lot. This is motivated by their relevance in many applications: elastography and medical imaging, seismology, potential theory, ion transport problems or chromatography, finances and other similar fields.

In this talk we will start recalling the meaning of inverse problems and the importance of studying their uniqueness. Then, we will explain the analytical and theoretical study of inverse problems where the goal is to determine or estimate the size of the spatial interval where the governing equation holds. We will focus here on the one-dimensional heat and wave equations and we will see that the uniqueness and the non-uniqueness are sensitive according to data settings.

If there is time for more, we will also show the numerical solutions to the inverse problems mentioned above and compute accurate approximations of the interval's sizes.

This is a joint research project in collaboration with Jin Cheng, Anna Doubova, Enrique Fernández-Cara and Masahiro Yamamoto.

Link to the session: https://zoom.us/j/95263362967?pwd=WmNVTjJ4Q3B2QW9aVEQzWjdxMTJTUT09

More info at https://sites.google.com/view/apdebilbao/home