Lipschitz stability in an inverse problem for the main coefficient of a Kuramoto–Sivashinsky type equation

In this paper we consider the inverse problem of retrieving the main coefficient of a Kuramoto–Sivashinsky type equation from partial knowledge of a given single solution. In particular, we focus on the stability issue of the inverse problem. By using a method due to Bukhgeim–Klibanov and suitable Carleman estimates, we obtain a local Lipschitz stability result on an admissible set of main coefficients. As a part of this study, we prove the existence of a unique solution to this equation.