On solution of the inverse coefficient heatconduction problem with a gradient projection method

An inverse coefficient heat conduction problem in layered medium is considered. Given boundary measurement data one has to determine thermal diffusivity coefficient. Direct problem operator that maps a thermal diffusivity coefficient to the boundary measurement data has been shown to have compact integral sensitivity operator (a generalization of the Freshet derivative). Investigation of the Lipshitzian properties of the sensitivity operator allowed to prove a theorem describing local convergence of the gradient projection method iterations to the solution of the inverse problem.