Acoustic wave guides as infinite-dimensional dynamical systems
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.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2012
- DOI:
- 10.48550/arXiv.1211.7000
- arXiv:
- arXiv:1211.7000
- Bibcode:
- 2012arXiv1211.7000A
- Keywords:
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- Mathematics - Dynamical Systems;
- Mathematics - Analysis of PDEs;
- Primary 35L05;
- secondary 35L20;
- 93C20;
- 47N70
- E-Print:
- 29 pp with Appendix 7pp