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Recovery of dipolar sources and stability estimates

Mdimagh Ridha (University of Jeddah, College of Science and Arts at Khulis, Department of Mathematics, Jeddah, Saudi Arabia + ENIT-LAMSIN, Tunis belvédère, University of Tunis El Manar, Tunisia)

The inverse problem of identifying dipolar sources with time-dependent moments, located in a bounded domain, via the heat equation is investigated, by applying a heat flux, and from a single lateral boundary measurement of temperature. An uniqueness, and local Lipschitz stability results for this inverse problem are established which are the main contributions of this work. A non-iterative algebraic algorithm based on the reciprocity gap concept is proposed, which permits to determine the number, the spatial locations, and the time-dependent moments of the dipolar sources, Some numerical experiments are given in order to test the efficiency and the robustness of this method.

Keywords: Heat equation, Inverse problem, Dipolar sources, Moments, Identifiability, Stability, Reciprocity gap functional