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Optimal regularity and optimal control of a thermoelastic structural acoustic model with point control and clamped boundary conditions

Lebiedzik C., Triggiani R.

Control and Cybernetics

2009

Vol. 38, no 4B

1461-1499

In this paper we consider point control of a structural acoustic model with thermoelastic effects. The key feature of this paper is that the two-dimensional plate modeling the active wall of the acoustic chamber has clamped boundary conditions. For this case a new optimal regularity result has recently become available (Triggiani, 2008). Using this new result for the plate alone, we derive a sharp (optimal) regularity result for the overall coupled system of wave and thermoelastic plate equations, after overcoming a series of additional technical difficulties. This allows for the study of an optimal control problem of the coupled system.

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.