Control Time for Gravity-Capillary Waves on Water

Abstract

This paper considers distributed open-loop control of small-amplitude linear waves on a fluid in which both surface tension and gravity are significant. It formulates the control system as a first-order evolution equation, reducing the null controllability problem to a moment problem involving frequency exponentials. For simple geometries in which eigenvalues can be calculated explicitly, controllability in arbitrary finite time is established, and aa relationship between mode frequencies and controller norm is noted.