Premium
Uniqueness and stable determination in the inverse Robin transmission problem with one electrostatic measurement
Author(s) -
Belhachmi Z.,
Meftahi H.
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3061
Subject(s) - uniqueness , mathematics , lipschitz continuity , inverse problem , inverse , stability (learning theory) , ball (mathematics) , upper and lower bounds , mathematical analysis , combinatorics , geometry , computer science , machine learning
In this paper, we consider the inverse Robin transmission problem with one electrostatic measurement. We prove a uniqueness result for the simultaneous determination of the Robin parameter p , the conductivity k , and the subdomain D , when D is a ball. When D and k are fixed, we prove a uniqueness result and a directional Lipschitz stability estimate for the Robin parameter p . When p and k are fixed, we give an upper bound to the subdomain D . For the reconstruction purposes of the Robin parameter p , we set the inverse problem under an optimization form for a Kohn–Vogelius cost functional. We prove the existence and the stability of the optimization problem. Finally, we show some numerical experiments that agree with the theoretical considerations. Copyright © 2013 John Wiley & Sons, Ltd.