Controllability for a One-Dimensional Wave Equation in a Non-cylindrical Domain

TL;DR

This paper investigates the controllability of a one-dimensional wave equation in a non-cylindrical domain, employing Stackelberg-Nash strategies to manage vibrations with fixed and moving endpoints.

Contribution

It introduces a novel control approach for wave equations in non-cylindrical domains using Stackelberg-Nash strategies, addressing boundary control with mixed conditions.

Findings

Established controllability results for the wave equation in non-cylindrical domains.

Applied Stackelberg-Nash strategies to boundary control problems.

Demonstrated effectiveness of the control method through theoretical analysis.

Abstract

This paper deals with the controllability for a one-dimensional wave equation with mixed boundary conditions in a non-cylindrical domain. This equation models small vibrations of a string where an endpoint is fixed and the other is moving. As usual, we consider one main control (the leader) and an additional secondary control (the follower). We use Stackelberg-Nash strategies.