Acoustic wave guides as infinite-dimensional dynamical systems

¹ Aalto University, Dept. Mathematics and Systems Analysis, P.O. Box 11100, 00076 Aalto, Finland.
jarmo.malinen@aalto.fi
² Department of Mathematics and Statistics, P.O. Box 35 (MaD), 40014 University of Jyväskylä, Finland.

Received: 20 December 2012
Revised: 28 February 2014

Abstract

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.