Acoustic wave guides as infinite-dimensional dynamical systems

TL;DR

This paper establishes mathematical properties like solvability and passivity for two models of acoustic wave propagation in curved tubular structures, linking 1D and 3D approaches in a unified framework.

Contribution

It provides a unified analysis of Webster's model and the 3D wave equation, demonstrating their mathematical properties and the connection between them.

Findings

Proves unique solvability of the models

Establishes passivity and conservativity of the systems

Shows the relation between 1D and 3D models in the limit

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.