Homogenization and two-scale convergence of the compressible Reynolds lubrication equation modelling the flying characteristics of a rough magnetic head over a rough rigid-disk surface

DOI10.1051/m2an/1995290201991zbMath0822.76078OpenAlexW249283481MaRDI QIDQ4834477

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Publication date: 5 October 1995

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/193772

zbMATH Keywords

existenceuniquenessslip flowrapidly oscillating coefficientslimit solutionsdouble-scale convergence

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Technical applications of optics and electromagnetic theory (78A55) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (17)

Homogenization of Reynolds equation by two-scale convergence ⋮ On the optimization of surface textures for lubricated contacts ⋮ Homogenization of a Reynolds equation describing compressible flow ⋮ Existence, uniqueness, and homogenization of the second order slip Reynolds equation. ⋮ Numerical solution of a 1-d elastohydrodynamic problem in magnetic storage devices ⋮ Analysis of the Reynolds equation for lubrication in case of pressure-dependent viscosity ⋮ Analysis of the effects of rough surfaces in compressible thin film flow by homogenization ⋮ Adaptive numerical methods for an hydrodynamic problem arising in magnetic reading devices ⋮ Homogenization of soft interfaces in time-dependent hydrodynamic lubrication ⋮ A Reduced Basis Method for the Homogenized Reynolds Equation Applied to Textured Surfaces ⋮ Influence of multiscale roughness patterns in cavitated flows: Applications to journal bearings ⋮ Existence and uniqueness of solutions of the parabolic nonlinear compressibel Reynolds lubrication equation ⋮ Homogenization of some variational problems connected to the theory of lubrication ⋮ A duality method for the compressible Reynolds equation. application to simulation of read/write processes in magnetic storage devices ⋮ A local discontinuous Galerkin method for the compressible Reynolds lubrication equation ⋮ Homogenization of nonlinear degenerate non-monotone elliptic operators in domains perforated with tiny holes ⋮ Homogenization of a class of nonlinear variational inequalities with applications in fluid film flow

Cites Work

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• Singular perturbation of initial-boundary value problems for a class of reaction diffusion systems
• Un résultat d'homogénéisation pour une classe de problèmes de diffusion non linéaires stationnaires
• On some nonlinear elliptic equations involving derivatives of the nonlinearity
• Existence and Uniqueness of Solutions to the Compressible Reynolds Lubrication Equation
• A Gas Film Lubrication Study—Part III: Experimental Investigation of Pivoted Slider Bearings
• A General Convergence Result for a Functional Related to the Theory of Homogenization

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