SIAM Journal on Control and Optimization, Volume 59, Issue 3, Page 1830-1850, January 2021.
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.

中文翻译：

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一维粘性自由边界流的可控性

SIAM控制与优化杂志，第59卷，第3期，第1830-1850页，2021
年1月。在这项工作中，我们解决了由粘性Burgers方程控制的流体的一维自由边界问题的局部可控性。自由边界表现为该间隔的一个运动端，其演化由该端点处的流体速度值给出。我们证明，通过控制沿固定边界的操作，除了规定自由边界的位置外，我们还可以将流体转向恒定速度，前提是初始速度和界面位置必须足够接近。