An integral constrained parabolic problem with applications in thermochronology

We investigate an inverse source problem with an integral constraint for a parabolic equation. The constraint is motivated by an application in thermochronology, a branch of geology. The existence and uniqueness of weak solutions are established by means of the Rothe method and an energy method, respectively. The elliptic problem resulting from the time discretization is solved by homogenizing the integral constraint. The implicit scheme used in the proof of existence lends itself readily for numerical studies and we present the results of numerical experiments. We also report on the errors and convergence rates.