Speaker: Sedar Ngoma

Title: Rothe's method for time-dependent inverse source / coefficient problems arising in geochronology.

Abstract: We investigate a problem arising in geochronology, the study of dating of rock formations and geological events, and in particular the reconstruction of temperature histories of rocks, and dating the cooling of rocks through exhumation. Reconstructing the temperature history amounts to solving a time-dependent, inverse coefficient problem for an integral constrained PDE. Using Rothe's method and an energy argument, we show the existence and uniqueness of weak solutions to the related inverse source problem. We describe numerical schemes which can be used to approximate solutions of the inverse problems and report on the errors and convergence rates. We also present the existence and uniqueness of a classical solution to the inverse source problem using the semigroup approach.