Analysis of a Sugimoto's model of nonlinear acoustics in an array of Helmholtz resonators

Abstract : A coupled system involving a nonlinear scalar PDE and a linear ODE is theoretically investigated. This hypebolic system with relaxation models the propagation of nonlinear waves in a waveguide connected to Helmholtz resonators, this device being an example of a nonlinear acoustic metamaterial. In a previous paper [Sugimoto, J. Fluid. Mech. 1992], it has been shown that this device allows also the propagation of acoustic solitons. In the present paper, the mathematical properties of the coupled system are analysed: formation of singularity in finite time, existence of global smooth solutions for small data, existence of entropy solutions in fractional BV spaces and uniqueness with a single family of entropies. New results are also deduced about weakly coupled systems. Numerical simulations illustrate these findings.
Complete list of metadatas

Cited literature [41 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02186692
Contributor : Bruno Lombard <>
Submitted on : Wednesday, July 17, 2019 - 1:41:00 PM
Last modification on : Thursday, July 25, 2019 - 1:22:15 AM

Files

Version1-HAL.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02186692, version 1

Citation

Stéphane Junca, Bruno Lombard. Analysis of a Sugimoto's model of nonlinear acoustics in an array of Helmholtz resonators. 2019. ⟨hal-02186692⟩

Share

Metrics

Record views

61

Files downloads

46