Inverse geometry problem for a 1D heat equation: a globality criterion

摘要

The n unknown lengths of a composite rod or plate are determined by measuring the n complex temperatures at ends of the 1D heat conduction model associated. The usual identification method by local minimization of a quadratic criterion is supplemented here by introduction of an original globality criterion of the local minimizer previously obtained. This criterion also provides a test for the existence of the solution in an arbitrary region of the field of research. These results provide a positive conclusion to a survey for two unknowns conducted in an earlier work. They are illustrated by two simulations, one for two unknowns, the other one for four unknowns.