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Proceedings Paper

Control problems in noise reduction: the case of two coupled hyperbolic equations
Author(s): Roberto Triggiani
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Paper 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.

Paper Details

Date Published: 13 June 1997
PDF: 11 pages
Proc. SPIE 3039, Smart Structures and Materials 1997: Mathematics and Control in Smart Structures, (13 June 1997); doi: 10.1117/12.276556
Show Author Affiliations
Roberto Triggiani, Univ. of Virginia (United States)

Published in SPIE Proceedings Vol. 3039:
Smart Structures and Materials 1997: Mathematics and Control in Smart Structures
Vasundara V. Varadan; Jagdish Chandra, Editor(s)

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