Open AccessRecovery of dipolar sources and stability estimates
Author(s) -
Ridha Mdimagh
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1913095m
Subject(s) - mathematics , bounded function , lipschitz continuity , robustness (evolution) , inverse problem , reciprocity (cultural anthropology) , uniqueness , inverse , stability (learning theory) , heat equation , mathematical analysis , algebraic number , dipole , geometry , computer science , psychology , social psychology , biochemistry , chemistry , organic chemistry , machine learning , gene
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.