Carleman estimates for the one-dimensional heat equation with a discontinuous coefficient and applications to controllability and an inverse problem - Archive ouverte HAL Access content directly
Journal Articles Journal of Mathematical Analysis and Applications Year : 2007

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

Assia Benabdallah
Yves Dermenjian
Jérôme Le Rousseau
• Function : Author
• PersonId : 2249
• IdHAL : jlr
• IdRef : 155029207

#### Abstract

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.

#### Domains

Mathematics [math] Analysis of PDEs [math.AP]

### Dates and versions

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

### Identifiers

• HAL Id : hal-00017486 , version 1
• DOI :

### Cite

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⟩

### Export

BibTeX TEI Dublin Core DC Terms EndNote Datacite

329 View