Abstract
For the homogeneous Euler equation linearized around a non-slipping mean flow and boundary conditions corresponding to the mass-spring-damper impedance, smooth initial data perturbations with compact support are considered. The propagation of this type of initial data perturbations in a straight cylindrical lined duct is investigated. Such kind of investigations is missing in the existing literature. The mathematical tools are the Fourier transform with respect to the axial spatial variable and the Laplace transform with respect to the time variable. The functional framework and sufficient conditions are researched that the so problem be well-posed in the sense of Hadamard and the Briggs-Bers stability criteria can be applied.
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