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Uniform stability in structural acoustic systems with thermal effects and nonlinear boundary damping

Lasiecka I., Lebiedzik C.

Control and Cybernetics

1999

Vol. 28, no 3

557-581

The stabilization problem for a structural acoustic model is considered. The model under consideration is that of acoustic cavity (wave equation) coupled at the interface with a flexible wall (plate equation) which accounts for thermal effects. It is shown that frictional, nonlinear damping applied at the boundary of the acoustic chamber provides the uniform decay rates for the energy function of the overall structure. The main novelty of this result, with respect to the literature, is that the uniform stability for the model is established without assuming any mechanical damping the wall.