Local controllability of the stabilized Kuramoto–Sivashinsky system by a single control acting on the heat equation

Abstract

In this paper we consider the so called stabilized Kuramoto–Sivashinsky system which couples a fourth order and a second order parabolic equations. We prove that this system is locally controllable to the trajectories by a single distributed control acting only on the heat equation. The main novelty is a new Carleman inequality for the solutions of a linear Kuramoto–Sivashinsky equation with nonhomogeneous boundary conditions.