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Article Dans Une Revue Journal of Mathematical Analysis and Applications Année : 2007

Carleman estimates for the one-dimensional heat equation with a discontinuous coefficient and applications to controllability and an inverse problem

Résumé

We study the observability and some of its consequences (controllability, identification of diffusion coefficients) for one-dimensional heat equations with discontinuous coefficients (piecewise $\Con^1$). The observability, for a linear equation, is obtained by a Carleman-type estimate. This kind of observability inequality yields controllability results for a semi-linear equation as well as a stability result for the identification of the diffusion coefficient.
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Dates et versions

hal-00017486 , version 1 (23-01-2006)

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Assia Benabdallah, Yves Dermenjian, Jérôme Le Rousseau. Carleman estimates for the one-dimensional heat equation with a discontinuous coefficient and applications to controllability and an inverse problem. Journal of Mathematical Analysis and Applications, 2007, 336 (2), pp.865-887. ⟨10.1016/j.jmaa.2007.03.024⟩. ⟨hal-00017486⟩
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