Boundary feedback stabilization of homogeneous equilibria in unstable fluid mixtures

We consider the problem of boundary feedback stabilization of homogeneous equilibria in unstable fluid mixtures that are governed by unstable linear reaction-convection-diffusion equations. We extend boundary feedback control laws designed for the one-dimensional reaction-diffusion equation using the backstepping method to this higher-dimensional case. We show that, under certain mathematical conditions on the velocity field, boundary feedback controls similar to the ones for one-dimensional equations also works for the higher dimensional case and exponentially stabilize the homogeneous equilibrium zero at any given decay rate.