Inverse heat conduction based on boundary measurement

This paper is concerned with the evaluation of the diffusion coefficient based on the measurement obtained at the boundary. We consider the problem of recovering the diffusion coefficient of a rod that is a function of space. The approach is based on allowing the unknown function to depend on time. With appropriate measurement data the unknown system parameters are guided from an arbitrary initial condition to their true value at a final time. An explicit equation describing the time evolution of the parameter is obtained by minimizing the error along the trajectory. The method leads to an iterative algorithm which is described in detail. In order to present the method in detail we first consider the problem of recovering a scalar heat generation which depends on the local temperature along the rod. Numerical results with the method indicate that close estimates of the unknown function can be obtained. Convergence of the method is also studied for a particular problem in inverse heat conduction.