Identification of non-smooth boundary heat dissipation by partial boundary data

When electronic devices are in operation, the sharp change of the temperature on devices surface can be considered as an indicator of devices faults. Based on this engineering background, we consider an inverse problem for 1-dimensional heat conduction model, with the aim of detecting the nonsmooth heat dissipation coefficient from measurable temperature on the device surface. We establish the uniqueness for the nonsmooth dissipation coefficient and prove the convergence property of the minimizer of the regularizing cost functional for the inverse problem theoretically. Then a double-iteration scheme minimizing the data-match term and the regularization term alternatively is proposed to implement the reconstructions.