Domain derivative approach to active infrared thermography

A thin conducting plate has an inaccessible side in contact with aggressive external agents. On the other side, we are able to heat the plate and take temperature maps in laboratory conditions. Detecting and evaluating damage on the inaccessible side from thermal data requires the solution of a nonlinear inverse problem for the heat equation in the presence of suitable boundary conditions for the heat equation. We carry on this task using domain derivative and integral formulation of the corresponding boundary value problem. Under non-restrictive hypothesis, we find explicit regularized schemes for Fourier reconstruction of damages.