Lipschitz stability in an inverse problem for the Kuramoto-Sivashinsky equation
نویسندگان
چکیده
In this article, we present 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 also at some positive time in the whole space domain. The Lipschitz stability for this inverse problem is our main result and it relies on the Bukhgĕım-Klibanov method. The proof is indeed based on a global Carleman estimate for the linearized K-S equation.
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