Carleman estimates for the one-dimensional heat equation with a discontinuous coefficient and applications
Résumé
We study the observability and some of its consequences for the one-dimensional heat equation with a discontinuous coefficient (piecewise $\Con^1$). The observability, for a {\em linear} equation, is obtained by a Carleman-type estimate. This kind of observability inequality yields results of controllability to the trajectories for {\em semilinear} equations. It also yields a stability result for the inverse problem of the identification of the diffusion coefficient.
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