Topological Asymptotic Analysis for a Time Fractional Identification Problem

ABSTRACT The aim of this work is the identification of the source term support from boundary measurements associated with a time‐fractional equation. The proposed approach is based on a combination between the Kohn‐Vogelius concept and the topological gradient method. The inverse problem is reformulated as an optimization one minimizing a Kohn‐Vogelius‐type functional. We derive a topological asymptotic formula describing the variation of the considered shape function with respect to a small geometric perturbation of the source term. The Riesz representation of the source term operator is determined and used in the calculation of the topological gradient expression.