Local controllability of the stabilized Kuramoto-Sivashinsky system by a single control acting on the heat equation (Q304877)

The paper is devoted to the so-called stabilized Kuramoto-Sivashinsky system that couples a fourth-order and a second-order parabolic equations. First, some well-posedness results concerning the systems under consideration are adduced. Then, the authors consider Carleman inequalities for the solutions of a linear Kuramoto-Sivashinsky equation with nonhomogeneous boundary conditions and give the proof of a new Carleman estimate. It is proved that the system is locally controllable to the trajectories by a single distributed control acting only on the heat equation.