Abstract
This paper considers the inverse problems of identifying either the unknown space-dependent heat source or the unknown time-dependent heat source of the variable coefficient advection–diffusion equation with separable sources of the form from supplementary time-dependent temperature measurement at the right boundary of the domain. We proved that solutions of both inverse source problems can be identified uniquely under some regularity assumptions. Two non-iterative inversion algorithms were developed and numerically implemented for the identification of the unknown space-wise and time-wise dependent sources. The robustness and limitations of the two algorithms are investigated through numerical examples related to the reconstruction of continuous and discontinuous sources.