Simultaneous controllability of wave sound propagations

TL;DR

This paper investigates the simultaneous controllability of sound wave systems in a fluid flow, establishing conditions under which both systems can be driven to equilibrium using a single control.

Contribution

It proves the well-posedness of the problem and identifies geometric and fluid assumptions enabling simultaneous control of sound propagation systems.

Findings

Well-posedness of the coupled sound systems

Conditions for simultaneous controllability

Single control driving both systems to equilibrium

Abstract

In this work we study one problem of mathematical interest for their applications in several topics in Applied Science. We study simultaneous controllability of a pair of systems which model the evolution of sound in a compressible ow considered as a transmission problem. We show the well posed of the problem. Furthermore provided appropriate conditions in the geometry of the domain are valid and suitable assumptions on the fluid, is possible to conduce the pair of systems to the equilibrium in a simultaneous way using only one control.