Propagation of the initial value perturbation in a cylindrical lined duct carrying a gas flow

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