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Article Dans Une Revue European Journal of Control Année : 2013

Coupling between hyperbolic and diffusive systems : a port-Hamiltonian formulation.

Résumé

The aim of this paper is to study a conservative wave equation coupled to a diffusion equation. This coupled system naturally arises in musical acoustics when viscous and thermal effects at the wall of the duct of a wind instrument are taken into account. The resulting equation, known as Webster-Lokshin model, has variable coefficients in space, and a fractional derivative in time. This equation can be recast into the port Hamiltonian framework by using the diffusive representation of the fractional derivative in time and a multiscale state space representation. The port-Hamiltonian formalism proves adequate to reformulate this coupled system, and could enable another well-posedness analysis, using classical results from port-Hamiltonian systems theory.
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Dates et versions

hal-00876852 , version 1 (25-10-2013)

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  • HAL Id : hal-00876852 , version 1

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Yann Le Gorrec, Denis Matignon. Coupling between hyperbolic and diffusive systems : a port-Hamiltonian formulation.. European Journal of Control, 2013, pp.1-9. ⟨hal-00876852⟩
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