Local Exact Controllability to the Trajectories of the Korteweg-de Vries-Burgers Equation on a Bounded Domain with Mixed Boundary Conditions

This paper studies the internal control of the Korteweg-de Vries-Burgers (KdVB) equation on a bounded domain. The diffusion coefficient is time-dependent and the boundary conditions are mixed in the sense that homogeneous Dirichlet and periodic Neumann boundary conditions are considered. The exact controllability to the trajectories is proven for a linearized system by using duality and getting a new Carleman estimate. Then, using an inversion theorem we deduce the local exact controllability to the trajectories for the original KdVB equation, which is nonlinear.