Identification of nonlinear heat conduction laws

Egger H., Pietschmann J., Schlottbom M.

Abstract

We consider the identification of nonlinear heat conduction laws in stationary and instationary heat transfer problems. Only a single additional measurement of the temperature on a curve on the boundary is required to determine the unknown parameter function on the range of observed temperatures. We first present a new proof of Cannon's uniqueness result for the stationary case, which allows us to derive a corresponding stability estimate, and then extend our argument to instationary problems which are close to steady state.