Acoustic wave guides as infinite-dimensional dynamical systems

Aalto, Atte; Lukkari, Teemu; Malinen, Jarmo

ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 2, pp. 324-347.

We prove the unique solvability, passivity/conservativity and some regularity results of two mathematical models for acoustic wave propagation in curved, variable diameter tubular structures of finite length. The first of the models is the generalised Webster’s model that includes dissipation and curvature of the 1D waveguide. The second model is the scattering passive, boundary controlled wave equation on 3D waveguides. The two models are treated in an unified fashion so that the results on the wave equation reduce to the corresponding results of approximating Webster’s model at the limit of vanishing waveguide intersection.

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