A new global Carleman estimate for the one-dimensional Kuramoto–Sivashinsky equation and applications to exact controllability to the trajectories and an inverse problem

In this paper, we establish a new global Carleman estimate for the linearized Kuramoto–Sivashinsky equation which is a one-parameter Carleman estimate. Based on this estimate, we can obtain the local exact controllability to the trajectories and Lipschitz stability in an inverse problem for the Kuramoto–Sivashinsky equation.