Numerical schemes for reconstructing profiles of moving sources in (time-fractional) evolution equations (Analysis of inverse problems through partial differential equations and related topics)

Abstract

This article is concerned with the derivation of numerical reconstruction schemes for the inverse moving source problem on determining source profiles in (time-fractional) evolution equations. As a continuation of the theoretical uniqueness, we adopt a minimization procedure with regularization to construct iterative thresholding schemes for the reduced backward problems on recovering one or two unknown initial value(s). Moreover, an elliptic approach is proposed to solving a convection equation in the case of two profiles.