Lipschitz stability in an inverse problem for the Kuramoto-Sivashinsky equation
Analysis of PDEs
2012-09-20 v3 Optimization and Control
Abstract
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.
Cite
@article{arxiv.1008.3279,
title = {Lipschitz stability in an inverse problem for the Kuramoto-Sivashinsky equation},
author = {Lucie Baudouin and Eduardo Cerpa and Emmanuelle Crépeau and Alberto Mercado},
journal= {arXiv preprint arXiv:1008.3279},
year = {2012}
}