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

In this article, we present an inverse problem for the nonlinear 1D Kuramoto-Sivashinsky (KS) 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 Bukhgem-Klibanov method. The proof is indeed based on a global Carleman estimate for the linearized KS equation.