B. Geshkovski, E. Zuazua. Controllability of one-dimensional viscous free boundary flows. Siam. J. Control. Optim. (2021)
Abstract. In this work, we address the local controllability of a one-dimensional free boundary problem for a fluid governed by the viscous Burgers equation. The free boundary manifests itself as one moving end of the interval, and its evolution is given by the value of the fluid velocity at this endpoint. We prove that, by means of a control actuating along the fixed boundary, we may steer the fluid to constant velocity in addition to prescribing the free boundary’s position, provided the initial velocities and interface positions are close enough.