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2008 An unconditional existence result for elastohydrodynamic piezoviscous lubrication problems with Elrod-Adams model of cavitation
Guy Bayada, Laurent Chupin, Bérénice Grec
Differential Integral Equations 21(1-2): 41-62 (2008).

Abstract

An unconditional existence result of a solution for a steady fluid-structure problem is stated. More precisely, we consider an incompressible fluid in a thin film, ruled by the Reynolds equation coupled with a surface deformation modelled by a nonlinear non local Hertz law. The viscosity is supposed to depend nonlinearly on the fluid pressure. Due to the apparition of a mushy region, the two-phase flow satisfies a free boundary problem defined by a pressure-saturation model. Such a problem has been studied with simpler free boundaries models (variational inequality), or with boundary conditions imposing small data assumptions. We show that up to a realistic hypothesis on the asymptotic pressure-viscosity behaviour it is possible to obtain an unconditional solution of the problem.

Citation

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Guy Bayada. Laurent Chupin. Bérénice Grec. "An unconditional existence result for elastohydrodynamic piezoviscous lubrication problems with Elrod-Adams model of cavitation." Differential Integral Equations 21 (1-2) 41 - 62, 2008.

Information

Published: 2008
First available in Project Euclid: 20 December 2012

zbMATH: 1224.35436
MathSciNet: MR2479661

Subjects:
Primary: 35Q35
Secondary: 74K35, 76D08

Rights: Copyright © 2008 Khayyam Publishing, Inc.

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Vol.21 • No. 1-2 • 2008
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