Perturbative methods in thermal imaging

I will discuss shortly three different inverse problems in the field of thermal nondestructive testing. In all cases we have a thin metallic plate $\Omega_0$ whose top boundary $S_{top}$ is not accessible while we are able to operate on the opposite surface $S_{bot}$.

We heat the specimen by applying a heat flux of density $\phi$ on $S_{bot}$ and measure a sequence of temperature maps.

Problem 1. Recover a perturbation of the heat transfer coefficient on $S_{top}$. [Inglese, Olmi - 2017]

Problem 2. Recover a surface damage on the inaccessible side $S_{top}$. [Inglese, Olmi - in progress]

Problem 3. Recover a nonlinear heat transfer coefficient on $S_{top}$. [Clarelli, Inglese - 2016]