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Carleman estimates for the one-dimensional heat equation with a discontinuous coefficient and applications to controllability and an inverse problem. (English) Zbl 1189.35349
Summary: We study the observability and some of its consequences (controllability, identification of diffusion coefficients) for one-dimensional heat equations with discontinuous coefficients (piecewise $${\mathcal C}^1$$). 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.

##### MSC:
 35R05 PDEs with low regular coefficients and/or low regular data 93B07 Observability 93B05 Controllability 35R30 Inverse problems for PDEs 35B45 A priori estimates in context of PDEs
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