ON GEOMETRIC INVERSE PROBLEMS IN TIME-FRACTIONAL SUBDIFFUSION

We consider two types of geometric shape inverse problems associated with time-fractional subdiffusion: the inverse source problem and interface reconstruction of a discontinuous subdiffusion coefficient. We show existence and present numerical methods for the two shape optimization model problems. We perform shape sensitivity analysis and use shape gradients to develop two numerical algorithms: a deformation algorithm and a level set method allowing both shape and topological changes. Numerical results are presented to demonstrate effectiveness of our algorithms.