SIMULTANEOUS IDENTIFICATION OF UNKNOWN INITIAL TEMPERATURE AND HEAT SOURCE

We investigate in this paper an ill-posed backward heat conduction problem of determining the unknown initial temperature and heat source from given observation at a fixed internal location and the solution value at terminal time. Unlike the classical single parameter identification problems, this ill-posed problem requires the determination of two independent unknown functions from scattered measurement of noisy data. Proof on the uniqueness of the solution is obtained by transforming the original heat conduction equation into an operator equation of the first kind. A new algorithm for the construction of the solution to the backward problem is derived by using the Landweber iteration method for the solution of the corresponding conjugate operator equation. Numerical verification on the efficiency and accuracy of the proposed algorithm is performed by solving several benchmark examples. The proposed method is readily extendable to solve more general multi-parameter identification problems.