Uniform decay rates for a variable-coefficient structural acoustic model with curved interface on a shallow shell. (English) Zbl 1526.76045
Summary: Uniform stabilization of a structural acoustic model describing an acoustic chamber with flexible curved wall is addressed. The coupled nonlinear system consists of a variable-coefficient wave equation and a shallow shell model which is used to model the flexible curved wall (interface). The coupling between the wave and the shell takes place on the interface. Derivation of stability estimates for the variable-coefficient coupled system with the shallow shell depends on the Riemannian geometry method and the multiplier technique. The uniform energy decay rates of the overall interactive model are achieved by introducing nonlinear boundary feedbacks applied to the wave equation and the shell model.
MSC:
| 76Q05 | Hydro- and aero-acoustics |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 74K25 | Shells |
| 35Q35 | PDEs in connection with fluid mechanics |
Keywords:
variable-coefficient wave equation; nonlinear boundary feedback; Riemannian geometry method; stability estimate; multiplier methodReferences:
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