Exact controllability of two-dimensional hydroelastic waves

TL;DR

This paper proves that two-dimensional hydroelastic waves can be precisely controlled in a short time when initial and final states are small, using exterior pressure supported on any open set.

Contribution

It establishes the exact controllability of 2D hydroelastic wave systems in a periodic setting with small initial and final data.

Findings

Exact controllability in short time for small data

Control achieved via exterior pressure on any open set

Applicable in periodic two-dimensional hydroelastic wave systems

Abstract

We prove the exact controllability of two-dimensional hydroelastic waves in the periodic setting. We show that if the initial data and the final data are small, for exterior pressure whose support is any non-empty open set $\omega$, the two-dimensional hydroelastic wave system is exactly controllable in arbitrary short time.