Control problems in noise reduction: the case of two coupled hyperbolic equations

Roberto Triggiani

doi:10.1117/12.276556

13 June 1997 Control problems in noise reduction: the case of two coupled hyperbolic equations

Roberto Triggiani

Proceedings Volume 3039, Smart Structures and Materials 1997: Mathematics and Control in Smart Structures; (1997) https://doi.org/10.1117/12.276556
Event: Smart Structures and Materials '97, 1997, San Diego, CA, United States

Abstract

We consider a mathematical model of the noise reduction problem, which couples tow hyperbolic equations: the wave equation in the interior - which describes the unwanted acoustic waves - and a Kirchoff equation - which models the vibrations of the elastic wall. In past models, the elastic wall was modeled by an Euleri-Bernoulli equation with Kelvin-Voight damping. Our main result is a sharp regularity result, in two dual versions, of the resulting system of two coupled hyperbolic PDE's. With this regularity results established, one can then invoke a wealth of abstract results on optimal control problems, min-max game theory. The proof of the main result is based on combining technical results.

Citation Download Citation

Roberto Triggiani "Control problems in noise reduction: the case of two coupled hyperbolic equations", Proc. SPIE 3039, Smart Structures and Materials 1997: Mathematics and Control in Smart Structures, (13 June 1997); https://doi.org/10.1117/12.276556

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available