Theoretical study of an abstract bubble vibration model
type: Item
instance of: scholarly article
title: Theoretical study of an abstract bubble vibration model
zbMATH Open document ID: 1262.35176
DOI: 10.4171/ZAA/1472
author: Yohan Penel
author: Stéphane Dellacherie
author: Olivier Lafitte
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2013-03-11T00:00:00Z
review text: Summary: We present the theoretical study of a hyperbolic-elliptic system of equations called the Abstract Bubble Vibration (ABV) model. This simplified system is derived from a model describing a diphasic low Mach number flow. It is thus aimed at providing mathematical properties of the coupling between the hyperbolic transport equation and the elliptic Poisson equation. We prove an existence and uniqueness result including the approximation of the time interval of existence for any smooth initial condition. In particular, we obtain a global-in-time existence result for small parameters. We then focus on properties of solutions (depending of their smoothness) such as maximum principle or evenness. In particular, an explicit formula of the mean value of solutions is given.
Mathematics Subject Classification ID: 35M30
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35A02
Mathematics Subject Classification ID: 35A09
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 6143104
zbMATH Keywords: short time existence
zbMATH Keywords: uniqueness
zbMATH Keywords: hyperbolic-elliptic system
zbMATH Keywords: diphasic low Mach number flow
zbMATH Keywords: explicit formula of the mean value
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.4171/zaa/1472
OpenAlex ID: W2054193152
description: scientific article; zbMATH DE number 6143104