Sentinels for the Identification of an Unknown Boundary

In this paper we have presented an eecient method to identify a part of the boundary of the domain for the heat equation. We formulated the problem as Jacques Simon did in 14] and we proposed a new identiication method. The theory used for the identiication needs the sentinels method developed by Lions 9], Kern evez 7] and Bodart 3]. And nally, we got a local convergence result for the iterative numerical scheme identifying the boundary. This result had been obtained in a constructive way, so we could implement the scheme and obtain satisfactory quantitative results. Furthermore we realized the numerical diiculties implied by this inverse problem. We have remarked that the solution of the optimization problem for the identiication was numerically unstable. This unstable solution has a direct consequence on the functions deened by the sentinels method : their norm is very large. It can therefore be expected that the identiication would be quite hard with noisy observations. Acknowledgments : The authors wish to thank J. Simon for valuable discussions.