Search results for " 93C20"

showing 2 items of 2 documents

Acoustic wave guides as infinite-dimensional dynamical systems

2015

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.

regularityControl and OptimizationDynamical systems theoryWave propagationwave propagationDynamical Systems (math.DS)Curvaturelaw.inventionMathematics - Analysis of PDEslawWebster’s horn modelFOS: MathematicspassivityMathematics - Dynamical SystemsMathematicstubular domainMathematical modelta111Mathematical analysisAcoustic waveDissipationWave equationPrimary 35L05 secondary 35L20 93C20 47N70Computational MathematicsControl and Systems Engineering: Mathematics [G03] [Physical chemical mathematical & earth Sciences]wave equation: Mathématiques [G03] [Physique chimie mathématiques & sciences de la terre]WaveguideAnalysis of PDEs (math.AP)ESAIM: Control, Optimisation and Calculus of Variations
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A posteriori error estimates for Webster's equation in wave propagation

2015

We consider a generalised Webster’s equation for describing wave propagation in curved tubular structures such as variable diameter acoustic wave guides. Webster’s equation in generalised form has been rigorously derived in a previous article starting from the wave equation, and it approximates cross-sectional averages of the propagating wave. Here, the approximation error is estimated by an a posteriori technique. peerReviewed

Wave propagationWave propagationApplied MathematicsMathematical analysista111Tubular domainDynamical Systems (math.DS)Acoustic waveWave equationPrimary 37L05. Secondary 35L05 35L20 47N70 93C20A posteriori error analysisMathematics - Analysis of PDEsApproximation errorFOS: MathematicsCalculusA priori and a posterioriWebster's modelMathematics - Dynamical SystemsAnalysisAnalysis of PDEs (math.AP)MathematicsVariable (mathematics)
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