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.

DOI: 10.1051/cocv/2014019

Keywords: Wave propagation, tubular domain, wave equation, Webster’s horn model, passivity, regularity

^{1}; Lukkari, Teemu

^{2}; Malinen, Jarmo

^{1}

@article{COCV_2015__21_2_324_0, author = {Aalto, Atte and Lukkari, Teemu and Malinen, Jarmo}, title = {Acoustic wave guides as infinite-dimensional dynamical systems}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {324--347}, publisher = {EDP-Sciences}, volume = {21}, number = {2}, year = {2015}, doi = {10.1051/cocv/2014019}, mrnumber = {3348400}, zbl = {1316.35165}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2014019/} }

TY - JOUR AU - Aalto, Atte AU - Lukkari, Teemu AU - Malinen, Jarmo TI - Acoustic wave guides as infinite-dimensional dynamical systems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2015 SP - 324 EP - 347 VL - 21 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2014019/ DO - 10.1051/cocv/2014019 LA - en ID - COCV_2015__21_2_324_0 ER -

%0 Journal Article %A Aalto, Atte %A Lukkari, Teemu %A Malinen, Jarmo %T Acoustic wave guides as infinite-dimensional dynamical systems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2015 %P 324-347 %V 21 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2014019/ %R 10.1051/cocv/2014019 %G en %F COCV_2015__21_2_324_0

Aalto, Atte; Lukkari, Teemu; Malinen, Jarmo. Acoustic wave guides as infinite-dimensional dynamical systems. ESAIM: Control, Optimisation and Calculus of Variations, Volume 21 (2015) no. 2, pp. 324-347. doi : 10.1051/cocv/2014019. http://archive.numdam.org/articles/10.1051/cocv/2014019/

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