On an hyperbolic system of nonlinear acoustics related to Helmholtz resonators
| Speaker |
Prof. Stéphane Junca
University of Nice Sophia-Antipolis
|
|---|---|
| When |
Mar 04, 2019
from 02:00 PM to 03:00 PM |
| Where | LH 006 |
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Abstract: A tube with Helmotz resonators is modelised by nonlinear PDEs with dissipative, dispersive and memory effects. Under some assumptions, the model can be reduced to a 3x3 nonlinear hyperbolic system. This system is a partially dissipative system endowed with a non increasing energy. Moreover, it can be rewritten as a Burgers
equation coupled with a linear operator representing a memory effect.
The modelisation is presented with numerical and mathematical studies, smooth solutions and shock apparitions. Moreover, the system admits large global solutions in the usual space BV of function of bounded variation and in a larger fractional BV space.Generalisations for a class of similar systems will be presented.
This is a joint work with Bruno Lombard, Labo. of Mechanics & Acoustics, CNRS, Marseill, France.