Orateur
Description
This conference delves into geometric inverse problems for partial differential equations, aiming to identify subdomains within multidimensional sets. We will explore two crucial aspects: uniqueness and numerical reconstruction. Several geometric inverse problems will be considered, some involving unknown initial data. Our primary focus will be on linear parabolic systems where the non-homogeneous part of the equation is expressed as a function of separate space and time variables. We establish uniqueness results by incorporating observations from the boundary or an interior domain, thereby deriving information about the initial data. The main tools for the proofs include unique continuation, time analyticity of solutions, and semigroup theory. Additionally, we will present some numerical results for reconstructing the unknown domain.
