Variable Support Control for the Wave Equation: A Multiplier Approach

TL;DR

This paper investigates controlling the multidimensional wave equation with a time-varying control support, using a multiplier method to establish observability and controllability results, with additional applications demonstrated.

Contribution

It introduces a novel approach to control support variation in wave equations and proves observability inequalities via a multiplier method.

Findings

Established controllability with variable support using multiplier techniques

Proved observability inequalities for the wave equation with changing control regions

Presented applications of the theoretical results

Abstract

We study the controllability of the multidimensional wave equation in a bounded domain with Dirichlet boundary condition, in which the support of the control is allowed to change over time. The exact controllability is reduced to the proof of the observability inequality, which is proven by a multiplier method. Besides our main results, we present some applications.