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13 June 1997 Control problems in noise reduction: the case of two coupled hyperbolic equations
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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.
© (1997) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
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
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