Sensibilité de l'équation de la chaleur aux sauts de conductivité

We investigate the differentiability of the solution of the heat equation with respect to the conductivity when this is piecewise continuous. We prove the existence of Lagrangian and punctual differentials and give their respective expressions. Finally, an application to the identification of a discontinuity is presented. Here, we propose an alternative method to the classical fast derivative method, which greatly simplifies the computations. To cite this article: O. Pantz, C. R. Acad. Sci. Paris, Ser. I 341 (2005).