Uniform Decay properties of a model in structural acoustics |
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Authors: | George Avalos Irena Lasiecka Richard Rebarber |
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Institution: | a Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409, USA;b Department of Mathematics, University of Virginia, Kerchof Hall, Charlottesville, VA 22903, USA;c Department of Mathematics and Statistics, University of Nebraska–Lincoln, Lincoln, NE 68588-0323, USA |
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Abstract: | We investigate decay properties for a system of coupled partial differential equations which model the interaction between acoustic waves in a cavity and the walls of the cavity. In this system a wave equation is coupled to a structurally damped plate or beam equation. The underlying semigroup for this system is not uniformly stable, but when the system is appropriately restricted we obtain some uniform stability. We present two results of this type. For the first result, we assume that the initial wave data is zero, and the initial plate or beam data is in the natural energy space; then the corresponding solution to system decays uniformly to zero. For the second result, we assume that the initial condition is in the natural energy space and the control function is L2(0,∞) (in time) into the control space; then the beam displacement and velocity are both L2(0,∞) into a space with two spatial derivatives. |
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Keywords: | Coupled partial differential equations Uniform stability Structural acoustics interactionsAuthor Keywords: Equations aux dé rivé es partielles couplé es Stabilité uniforme Interactions acoustiques structurelles |
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