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Article Dans Une Revue Applicable Analysis Année : 2013

Lipschitz stability in an inverse problem for the Kuramoto-Sivashinsky equation

Résumé

This paper presents an inverse problem for the nonlinear 1-d Kuramoto-Sivashinsky (K-S) equation. More precisely, we study the nonlinear inverse problem of retrieving the anti-diffusion coefficient from the measurements of the solution on a part of the boundary and at some positive time everywhere. Uniqueness and Lipschitz stability for this inverse problem are proven with the Bukhgeim-Klibanov method. The proof is based on a global Carleman estimate for the linearized K-S equation.
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Dates et versions

hal-00510506 , version 1 (19-08-2010)
hal-00510506 , version 2 (06-10-2011)
hal-00510506 , version 3 (19-09-2012)

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Lucie Baudouin, Eduardo Cerpa, Emmanuelle Crépeau, Alberto Mercado. Lipschitz stability in an inverse problem for the Kuramoto-Sivashinsky equation. Applicable Analysis, 2013, 92 (10), pp. 2084-2102. ⟨hal-00510506v3⟩
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