The transient lubrication problem as a generalized Hele-Shaw type problem
type: Item
instance of: scholarly article
title: The transient lubrication problem as a generalized Hele-Shaw type problem
zbMATH Open document ID: 0829.35094
DOI: 10.4171/ZAA/663
author: Mahdi Boukrouche
author: Mohamed El Alaoui Talibi
author: Guy Bayada
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1995-04-23T00:00:00Z
review text: The connection between the Hele-Shaw type problem and the lubrication problem is considered in this paper. The authors reformulate the first generalization of the Hele-Shaw problem as a time dependent variational inequality. To guarantee the equivalence between the strong and the weak formulation of the Hele-Shaw type problem, some new regularity results for the time dependent variational inequality of the first kind are established. The weak formulation for the lubrication problem with shear effects is deduced. In the case of the absence of shear effects, the uniqueness of the weak solution for the lubrication problem is obtained by a second abstract variational approach. Finally, the authors prove that the solution of the weak formulation of both Hele-Shaw type problems and shearless lubrication problems are the same, which means the Hele-Shaw phenomena can be regarded as a particular case of lubrication problem.
reviewed by: Ding Zhengzhong
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 76D08
Mathematics Subject Classification ID: 76B10
Mathematics Subject Classification ID: 76E30
Mathematics Subject Classification ID: 76M30
zbMATH DE Number: 739094
zbMATH Keywords: Hele-Shaw flow
zbMATH Keywords: cavitation phenomena
zbMATH Keywords: variational inequality
zbMATH Keywords: lubrication problem
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.4171/zaa/663
OpenAlex ID: W2055227316
description: scientific article; zbMATH DE number 739094