Existence and uniqueness of a solution to an aeroacoustic model
type: Item
instance of: scholarly article
title: Existence and uniqueness of a solution to an aeroacoustic model
zbMATH Open document ID: 1007.35078
DOI: 10.1142/S0252959902000031
author: Emmanuelle Gout-D'Hénin
author: Philippe Destuynder
published in: Chinese Annals of Mathematics. Series B
publication date: 2003-03-20T00:00:00Z
review text: The authors consider a linear theory of the propagation of three-dimensional aeroacoustic waves near a flexible structure (here a flat membrane). The fluid flow is described by a potential function. Using Steklov eigenvalue analysis, the authors prove the existence and uniqueness of a solution under a seemingly restrictive assumption on the flow velocity. But a counter example proves that this restriction is also necessary.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76Q05
Mathematics Subject Classification ID: 74F10
Mathematics Subject Classification ID: 74H20
zbMATH DE Number: 1751698
zbMATH Keywords: linear theory
zbMATH Keywords: three-dimensional aeroacoustic waves
zbMATH Keywords: flexible structure
zbMATH Keywords: flat membrane
zbMATH Keywords: potential function
zbMATH Keywords: Steklov eigenvalue analysis
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
MaRDI profile type: Publication
cites work: Numerical solution of conservation equations arising in linear wave theory: application to aeroacoustics
cites work: A linear model of a finite amplitude Helmholtz instability
description: scientific article; zbMATH DE number 1751698